176Complex<double> result = new Complex<double>(left.m_real, left.m_imaginary) * right; 182Complex<double> result = left * new Complex<double>(right.m_real, right.m_imaginary); 188Complex<double> result = new Complex<double>(left.m_real, left.m_imaginary) / new Complex<double>(right.m_real, right.m_imaginary); 194Complex<double> result = new Complex<double>(left.m_real, left.m_imaginary) / right; 200Complex<double> result = left / new Complex<double>(right.m_real, right.m_imaginary); 254=> new Complex<double>(m_real, m_imaginary).ToString(format, provider); 275Complex<double> result = Complex<double>.Asin(new Complex<double>(value.m_real, value.m_imaginary)); 293Complex<double> result = Complex<double>.Acos(new Complex<double>(value.m_real, value.m_imaginary)); 299Complex<double> result = Complex<double>.Tan(new Complex<double>(value.m_real, value.m_imaginary)); 346Complex<double> result = Complex<double>.Sqrt(new Complex<double>(value.m_real, value.m_imaginary)); 352Complex<double> result = Complex<double>.Pow(new Complex<double>(value.m_real, value.m_imaginary), new Complex<double>(power.m_real, power.m_imaginary)); 681Complex<double> result = Complex<double>.MaxMagnitude(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 688Complex<double> result = Complex<double>.MaxMagnitudeNumber(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 695Complex<double> result = Complex<double>.MinMagnitude(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 702Complex<double> result = Complex<double>.MinMagnitudeNumber(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 709Complex<double> result = Complex<double>.MultiplyAddEstimate(new Complex<double>(left.m_real, left.m_imaginary), new Complex<double>(right.m_real, right.m_imaginary), new Complex<double>(addend.m_real, addend.m_imaginary)); 787result = (TOther)(object)new Complex<double>(value.m_real, value.m_imaginary); 791return Complex<double>.TryConvertToCheckedCore(new Complex<double>(value.m_real, value.m_imaginary), out result); 800result = (TOther)(object)new Complex<double>(value.m_real, value.m_imaginary); 804return Complex<double>.TryConvertToSaturatingCore(new Complex<double>(value.m_real, value.m_imaginary), out result); 813result = (TOther)(object)new Complex<double>(value.m_real, value.m_imaginary); 817return Complex<double>.TryConvertToTruncatingCore(new Complex<double>(value.m_real, value.m_imaginary), out result);

26public static Complex<T> Zero => new(T.Zero, T.Zero); 27public static Complex<T> One => new(T.One, T.Zero); 28public static Complex<T> ImaginaryOne => new(T.Zero, T.One); 29public static Complex<T> NaN => new(T.NaN, T.NaN); 30public static Complex<T> Infinity => new(T.PositiveInfinity, T.PositiveInfinity); 62return new Complex<T>(magnitude * cos, magnitude * sin); 132return new Complex<T>(-value.m_real, -value.m_imaginary); 137return new Complex<T>(left.m_real + right.m_real, left.m_imaginary + right.m_imaginary); 142return new Complex<T>(left.m_real + right, left.m_imaginary); 147return new Complex<T>(left + right.m_real, right.m_imaginary); 152return new Complex<T>(left.m_real - right.m_real, left.m_imaginary - right.m_imaginary); 157return new Complex<T>(left.m_real - right, left.m_imaginary); 162return new Complex<T>(left - right.m_real, -right.m_imaginary); 170return new Complex<T>(result_realpart, result_imaginarypart); 179return new Complex<T>(T.NaN, T.NaN); 182return new Complex<T>(left.m_real * right, T.NaN); 187return new Complex<T>(T.NaN, left.m_imaginary * right); 190return new Complex<T>(left.m_real * right, left.m_imaginary * right); 199return new Complex<T>(T.NaN, T.NaN); 202return new Complex<T>(left * right.m_real, T.NaN); 207return new Complex<T>(T.NaN, left * right.m_imaginary); 210return new Complex<T>(left * right.m_real, left * right.m_imaginary); 225return new Complex<T>((a + b * doc) / (c + d * doc), (b - a * doc) / (c + d * doc)); 230return new Complex<T>((b + a * cod) / (d + c * cod), (-a + b * cod) / (d + c * cod)); 241return new Complex<T>(T.NaN, T.NaN); 248return new Complex<T>(T.NaN, T.NaN); 251return new Complex<T>(left.m_real / right, T.NaN); 256return new Complex<T>(T.NaN, left.m_imaginary / right); 260return new Complex<T>(left.m_real / right, left.m_imaginary / right); 274return new Complex<T>(a / (c + d * doc), (-a * doc) / (c + d * doc)); 279return new Complex<T>(a * cod / (d + c * cod), -a / (d + c * cod)); 316return new Complex<T>(value.m_real, -value.m_imaginary); 372return new Complex<T>(sin * T.Cosh(value.m_imaginary), cos * T.Sinh(value.m_imaginary)); 378Complex<T> sin = Sin(new Complex<T>(-value.m_imaginary, value.m_real)); 379return new Complex<T>(sin.m_imaginary, -sin.m_real); 399return new Complex<T>(u, v); 405return new Complex<T>(cos * T.Cosh(value.m_imaginary), -sin * T.Sinh(value.m_imaginary)); 411return Cos(new Complex<T>(-value.m_imaginary, value.m_real)); 431return new Complex<T>(u, v); 453return new Complex<T>(sin / D, T.Sinh(y2) / D); 458return new Complex<T>(sin / cosh / D, T.Tanh(y2) / D); 465Complex<T> tan = Tan(new Complex<T>(-value.m_imaginary, value.m_real)); 466return new Complex<T>(tan.m_imaginary, -tan.m_real); 471Complex<T> two = new(T.CreateChecked(2), T.Zero); 566return new Complex<T>(T.Log(Abs(value)), T.Atan2(value.m_imaginary, value.m_real)); 571return Log(value) / Log(new Complex<T>(baseValue, T.Zero)); 593return new Complex<T>(T.PositiveInfinity, value.m_imaginary); 595return new Complex<T>(T.NaN, T.NaN); 601return new Complex<T>(T.NaN, T.PositiveInfinity); 605return new Complex<T>(T.PositiveInfinity, T.NaN); 607return new Complex<T>(T.NaN, T.NaN); 615return new Complex<T>(T.Zero, T.Sqrt(-value.m_real)); 618return new Complex<T>(T.Sqrt(value.m_real), T.Zero); 633return new Complex<T>(T.PositiveInfinity, imaginaryCopy); 663return new Complex<T>(x, y); 694return Pow(value, new Complex<T>(power, T.Zero)); 701return new Complex<T>(realResult, imaginaryResult); 710return new Complex<T>(value, T.Zero); 1155return new Complex<T>(result_realpart, result_imaginarypart); 1215result = new Complex<T>((T)(object)value, T.Zero); 1222result = new Complex<T>(T.CreateChecked(actualValue.Real), T.CreateChecked(actualValue.Imaginary)); 1228result = new Complex<T>(realResult, T.Zero); 1234result = new Complex<T>(realResult2, T.Zero); 1247result = new Complex<T>((T)(object)value, T.Zero); 1254result = new Complex<T>(T.CreateSaturating(actualValue.Real), T.CreateSaturating(actualValue.Imaginary)); 1260result = new Complex<T>(realResult, T.Zero); 1266result = new Complex<T>(realResult2, T.Zero); 1279result = new Complex<T>((T)(object)value, T.Zero); 1286result = new Complex<T>(T.CreateTruncating(actualValue.Real), T.CreateTruncating(actualValue.Imaginary)); 1292result = new Complex<T>(realResult, T.Zero); 1298result = new Complex<T>(realResult2, T.Zero); 1564result = new Complex<T>(real!, imaginary!); 1614static Complex<T> ISignedNumber<Complex<T>>.NegativeOne => new(-T.One, T.Zero);

176Complex<double> result = new Complex<double>(left.m_real, left.m_imaginary) * right; 182Complex<double> result = left * new Complex<double>(right.m_real, right.m_imaginary); 188Complex<double> result = new Complex<double>(left.m_real, left.m_imaginary) / new Complex<double>(right.m_real, right.m_imaginary); 194Complex<double> result = new Complex<double>(left.m_real, left.m_imaginary) / right; 200Complex<double> result = left / new Complex<double>(right.m_real, right.m_imaginary); 275Complex<double> result = Complex<double>.Asin(new Complex<double>(value.m_real, value.m_imaginary)); 293Complex<double> result = Complex<double>.Acos(new Complex<double>(value.m_real, value.m_imaginary)); 299Complex<double> result = Complex<double>.Tan(new Complex<double>(value.m_real, value.m_imaginary)); 346Complex<double> result = Complex<double>.Sqrt(new Complex<double>(value.m_real, value.m_imaginary)); 352Complex<double> result = Complex<double>.Pow(new Complex<double>(value.m_real, value.m_imaginary), new Complex<double>(power.m_real, power.m_imaginary)); 681Complex<double> result = Complex<double>.MaxMagnitude(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 688Complex<double> result = Complex<double>.MaxMagnitudeNumber(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 695Complex<double> result = Complex<double>.MinMagnitude(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 702Complex<double> result = Complex<double>.MinMagnitudeNumber(new Complex<double>(x.m_real, x.m_imaginary), new Complex<double>(y.m_real, y.m_imaginary)); 709Complex<double> result = Complex<double>.MultiplyAddEstimate(new Complex<double>(left.m_real, left.m_imaginary), new Complex<double>(right.m_real, right.m_imaginary), new Complex<double>(addend.m_real, addend.m_imaginary)); 764if (typeof(TOther) == typeof(Complex<double>)) 766Complex<double> actualValue = (Complex<double>)(object)value; 771if (Complex<double>.TryConvertFromCheckedCore(value, out Complex<double> intermediate)) 785if (typeof(TOther) == typeof(Complex<double>)) 791return Complex<double>.TryConvertToCheckedCore(new Complex<double>(value.m_real, value.m_imaginary), out result); 798if (typeof(TOther) == typeof(Complex<double>)) 804return Complex<double>.TryConvertToSaturatingCore(new Complex<double>(value.m_real, value.m_imaginary), out result); 811if (typeof(TOther) == typeof(Complex<double>)) 817return Complex<double>.TryConvertToTruncatingCore(new Complex<double>(value.m_real, value.m_imaginary), out result); 824return Complex<double>.TryParse(MemoryMarshal.Cast<char, Utf16Char>(s), style, provider, out Unsafe.As<Complex, Complex<double>>(ref result), out _); 831return Complex<double>.TryParse(MemoryMarshal.Cast<byte, Utf8Char>(utf8Text), style, provider, out Unsafe.As<Complex, Complex<double>>(ref result), out _); 838return Complex<double>.TryParse(MemoryMarshal.Cast<char, Utf16Char>(s.AsSpan()), style, provider, out Unsafe.As<Complex, Complex<double>>(ref result), out charsConsumed); 845return Complex<double>.TryParse(MemoryMarshal.Cast<byte, Utf8Char>(utf8Text), style, provider, out Unsafe.As<Complex, Complex<double>>(ref result), out bytesConsumed); 852return Complex<double>.TryParse(MemoryMarshal.Cast<char, Utf16Char>(s), style, provider, out Unsafe.As<Complex, Complex<double>>(ref result), out charsConsumed);

19: IEquatable<Complex<T>>, 21INumberBase<Complex<T>>, 22ISignedNumber<Complex<T>>, 26public static Complex<T> Zero => new(T.Zero, T.Zero); 27public static Complex<T> One => new(T.One, T.Zero); 28public static Complex<T> ImaginaryOne => new(T.Zero, T.One); 29public static Complex<T> NaN => new(T.NaN, T.NaN); 30public static Complex<T> Infinity => new(T.PositiveInfinity, T.PositiveInfinity); 59public static Complex<T> FromPolarCoordinates(T magnitude, T phase) 65public static Complex<T> Negate(Complex<T> value) 70public static Complex<T> Add(Complex<T> left, Complex<T> right) 75public static Complex<T> Add(Complex<T> left, T right) 80public static Complex<T> Add(T left, Complex<T> right) 85public static Complex<T> Subtract(Complex<T> left, Complex<T> right) 90public static Complex<T> Subtract(Complex<T> left, T right) 95public static Complex<T> Subtract(T left, Complex<T> right) 100public static Complex<T> Multiply(Complex<T> left, Complex<T> right) 105public static Complex<T> Multiply(Complex<T> left, T right) 110public static Complex<T> Multiply(T left, Complex<T> right) 115public static Complex<T> Divide(Complex<T> dividend, Complex<T> divisor) 120public static Complex<T> Divide(Complex<T> dividend, T divisor) 125public static Complex<T> Divide(T dividend, Complex<T> divisor) 130public static Complex<T> operator -(Complex<T> value) 135public static Complex<T> operator +(Complex<T> left, Complex<T> right) 140public static Complex<T> operator +(Complex<T> left, T right) 145public static Complex<T> operator +(T left, Complex<T> right) 150public static Complex<T> operator -(Complex<T> left, Complex<T> right) 155public static Complex<T> operator -(Complex<T> left, T right) 160public static Complex<T> operator -(T left, Complex<T> right) 165public static Complex<T> operator *(Complex<T> left, Complex<T> right) 173public static Complex<T> operator *(Complex<T> left, T right) 193public static Complex<T> operator *(T left, Complex<T> right) 213public static Complex<T> operator /(Complex<T> left, Complex<T> right) 234public static Complex<T> operator /(Complex<T> left, T right) 263public static Complex<T> operator /(T left, Complex<T> right) 283public static T Abs(Complex<T> value) 313public static Complex<T> Conjugate(Complex<T> value) 319public static Complex<T> Reciprocal(Complex<T> value) 329public static bool operator ==(Complex<T> left, Complex<T> right) 334public static bool operator !=(Complex<T> left, Complex<T> right) 341return obj is Complex<T> other && Equals(other); 344public bool Equals(Complex<T> value) 369public static Complex<T> Sin(Complex<T> value) 375public static Complex<T> Sinh(Complex<T> value) 378Complex<T> sin = Sin(new Complex<T>(-value.m_imaginary, value.m_real)); 382public static Complex<T> Asin(Complex<T> value) 402public static Complex<T> Cos(Complex<T> value) 408public static Complex<T> Cosh(Complex<T> value) 414public static Complex<T> Acos(Complex<T> value) 434public static Complex<T> Tan(Complex<T> value) 462public static Complex<T> Tanh(Complex<T> value) 465Complex<T> tan = Tan(new Complex<T>(-value.m_imaginary, value.m_real)); 469public static Complex<T> Atan(Complex<T> value) 471Complex<T> two = new(T.CreateChecked(2), T.Zero); 558public static bool IsFinite(Complex<T> value) => T.IsFinite(value.m_real) && T.IsFinite(value.m_imaginary); 560public static bool IsInfinity(Complex<T> value) => T.IsInfinity(value.m_real) || T.IsInfinity(value.m_imaginary); 562public static bool IsNaN(Complex<T> value) => !IsInfinity(value) && !IsFinite(value); 564public static Complex<T> Log(Complex<T> value) 569public static Complex<T> Log(Complex<T> value, T baseValue) 574public static Complex<T> Log10(Complex<T> value) 576Complex<T> tempLog = Log(value); 580public static Complex<T> Exp(Complex<T> value) 586public static Complex<T> Sqrt(Complex<T> value) 666public static Complex<T> Pow(Complex<T> value, Complex<T> power) 692public static Complex<T> Pow(Complex<T> value, T power) 697private static Complex<T> Scale(Complex<T> value, T factor) 708public static implicit operator Complex<T>(T value) 718static Complex<T> IAdditiveIdentity<Complex<T>, Complex<T>>.AdditiveIdentity => Zero; 725public static Complex<T> operator --(Complex<T> value) => value - One; 732public static Complex<T> operator ++(Complex<T> value) => value + One; 739static Complex<T> IMultiplicativeIdentity<Complex<T>, Complex<T>>.MultiplicativeIdentity => One; 746static int INumberBase<Complex<T>>.Radix => T.Radix; 749static Complex<T> INumberBase<Complex<T>>.Abs(Complex<T> value) => Abs(value); 753public static Complex<T> CreateChecked<TOther>(TOther value) 756Complex<T> result; 758if (typeof(TOther) == typeof(Complex<T>)) 760result = (Complex<T>)(object)value; 772public static Complex<T> CreateSaturating<TOther>(TOther value) 775Complex<T> result; 777if (typeof(TOther) == typeof(Complex<T>)) 779result = (Complex<T>)(object)value; 791public static Complex<T> CreateTruncating<TOther>(TOther value) 794Complex<T> result; 796if (typeof(TOther) == typeof(Complex<T>)) 798result = (Complex<T>)(object)value; 809static bool INumberBase<Complex<T>>.IsCanonical(Complex<T> value) => true; 812public static bool IsComplexNumber(Complex<T> value) => (value.m_real != T.Zero) && (value.m_imaginary != T.Zero); 815public static bool IsEvenInteger(Complex<T> value) => (value.m_imaginary == T.Zero) && T.IsEvenInteger(value.m_real); 818public static bool IsImaginaryNumber(Complex<T> value) => (value.m_real == T.Zero) && T.IsRealNumber(value.m_imaginary); 821public static bool IsInteger(Complex<T> value) => (value.m_imaginary == T.Zero) && T.IsInteger(value.m_real); 824public static bool IsNegative(Complex<T> value) 833public static bool IsNegativeInfinity(Complex<T> value) 842public static bool IsNormal(Complex<T> value) 852public static bool IsOddInteger(Complex<T> value) => (value.m_imaginary == T.Zero) && T.IsOddInteger(value.m_real); 855public static bool IsPositive(Complex<T> value) 864public static bool IsPositiveInfinity(Complex<T> value) 873public static bool IsRealNumber(Complex<T> value) => (value.m_imaginary == T.Zero) && T.IsRealNumber(value.m_real); 876public static bool IsSubnormal(Complex<T> value) 885static bool INumberBase<Complex<T>>.IsZero(Complex<T> value) => (value.m_real == T.Zero) && (value.m_imaginary == T.Zero); 888public static Complex<T> MaxMagnitude(Complex<T> x, Complex<T> y) 957internal static Complex<T> MaxMagnitudeNumber(Complex<T> x, Complex<T> y) 1014static Complex<T> INumberBase<Complex<T>>.MaxMagnitudeNumber(Complex<T> x, Complex<T> y) 1018public static Complex<T> MinMagnitude(Complex<T> x, Complex<T> y) 1078internal static Complex<T> MinMagnitudeNumber(Complex<T> x, Complex<T> y) 1139static Complex<T> INumberBase<Complex<T>>.MinMagnitudeNumber(Complex<T> x, Complex<T> y) 1142internal static Complex<T> MultiplyAddEstimate(Complex<T> left, Complex<T> right, Complex<T> addend) 1159static Complex<T> INumberBase<Complex<T>>.MultiplyAddEstimate(Complex<T> left, Complex<T> right, Complex<T> addend) 1163public static Complex<T> Parse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider? provider) 1165if (!TryParse(s, style, provider, out Complex<T> result)) 1173public static Complex<T> Parse(ReadOnlySpan<byte> utf8Text, NumberStyles style, IFormatProvider? provider) 1175if (!TryParse(utf8Text, style, provider, out Complex<T> result)) 1183public static Complex<T> Parse(string s, NumberStyles style, IFormatProvider? provider) 1191static bool INumberBase<Complex<T>>.TryConvertFromChecked<TOther>(TOther value, out Complex<T> result) 1198static bool INumberBase<Complex<T>>.TryConvertFromSaturating<TOther>(TOther value, out Complex<T> result) 1205static bool INumberBase<Complex<T>>.TryConvertFromTruncating<TOther>(TOther value, out Complex<T> result) 1210internal static bool TryConvertFromCheckedCore<TOther>(TOther value, out Complex<T> result) 1242internal static bool TryConvertFromSaturatingCore<TOther>(TOther value, out Complex<T> result) 1274internal static bool TryConvertFromTruncatingCore<TOther>(TOther value, out Complex<T> result) 1308static bool INumberBase<Complex<T>>.TryConvertToChecked<TOther>(Complex<T> value, [MaybeNullWhen(false)] out TOther result) 1310if (typeof(TOther) == typeof(Complex<T>)) 1321static bool INumberBase<Complex<T>>.TryConvertToSaturating<TOther>(Complex<T> value, [MaybeNullWhen(false)] out TOther result) 1323if (typeof(TOther) == typeof(Complex<T>)) 1334static bool INumberBase<Complex<T>>.TryConvertToTruncating<TOther>(Complex<T> value, [MaybeNullWhen(false)] out TOther result) 1336if (typeof(TOther) == typeof(Complex<T>)) 1345internal static bool TryConvertToCheckedCore<TOther>(Complex<T> value, [MaybeNullWhen(false)] out TOther result) 1392internal static bool TryConvertToSaturatingCore<TOther>(Complex<T> value, [MaybeNullWhen(false)] out TOther result) 1423internal static bool TryConvertToTruncatingCore<TOther>(Complex<T> value, [MaybeNullWhen(false)] out TOther result) 1455public static bool TryParse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider? provider, out Complex<T> result) 1459public static bool TryParse(ReadOnlySpan<byte> utf8Text, NumberStyles style, IFormatProvider? provider, out Complex<T> result) 1463static bool INumberBase<Complex<T>>.TryParse([NotNullWhen(true)] string? s, NumberStyles style, IFormatProvider? provider, out Complex<T> result, out int charsConsumed) 1467static bool INumberBase<Complex<T>>.TryParse(ReadOnlySpan<byte> utf8Text, NumberStyles style, IFormatProvider? provider, out Complex<T> result, out int bytesConsumed) 1471static bool INumberBase<Complex<T>>.TryParse(ReadOnlySpan<char> s, NumberStyles style, IFormatProvider? provider, out Complex<T> result, out int charsConsumed) 1474internal static bool TryParse<TChar>(ReadOnlySpan<TChar> text, NumberStyles style, IFormatProvider? provider, out Complex<T> result, out int elementsConsumed) 1589public static bool TryParse([NotNullWhen(true)] string? s, NumberStyles style, IFormatProvider? provider, out Complex<T> result) 1604public static Complex<T> Parse(string s, IFormatProvider? provider) => Parse(s, Complex.DefaultNumberStyle, provider); 1607public static bool TryParse([NotNullWhen(true)] string? s, IFormatProvider? provider, out Complex<T> result) => TryParse(s, Complex.DefaultNumberStyle, provider, out result); 1614static Complex<T> ISignedNumber<Complex<T>>.NegativeOne => new(-T.One, T.Zero); 1674public static Complex<T> Parse(ReadOnlySpan<char> s, IFormatProvider? provider) => Parse(s, Complex.DefaultNumberStyle, provider); 1677public static bool TryParse(ReadOnlySpan<char> s, IFormatProvider? provider, out Complex<T> result) => TryParse(s, Complex.DefaultNumberStyle, provider, out result); 1684public static Complex<T> operator +(Complex<T> value) => value; 1691public static Complex<T> Parse(ReadOnlySpan<byte> utf8Text, IFormatProvider? provider) => Parse(utf8Text, Complex.DefaultNumberStyle, provider); 1694public static bool TryParse(ReadOnlySpan<byte> utf8Text, IFormatProvider? provider, out Complex<T> result) => TryParse(utf8Text, Complex.DefaultNumberStyle, provider, out result);