50m_imaginary = imaginary;

54public T Imaginary => m_imaginary; 57public T GetPhase() => T.Atan2(m_imaginary, m_real); 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); 168T result_realpart = (left.m_real * right.m_real) - (left.m_imaginary * right.m_imaginary); 169T result_imaginarypart = (left.m_imaginary * right.m_real) + (left.m_real * right.m_imaginary); 177if (!T.IsFinite(left.m_imaginary)) 185if (!T.IsFinite(left.m_imaginary)) 187return new Complex<T>(T.NaN, left.m_imaginary * right); 190return new Complex<T>(left.m_real * right, left.m_imaginary * right); 197if (!T.IsFinite(right.m_imaginary)) 205if (!T.IsFinite(right.m_imaginary)) 207return new Complex<T>(T.NaN, left * right.m_imaginary); 210return new Complex<T>(left * right.m_real, left * right.m_imaginary); 217T b = left.m_imaginary; 219T d = right.m_imaginary; 246if (!T.IsFinite(left.m_imaginary)) 254if (!T.IsFinite(left.m_imaginary)) 256return new Complex<T>(T.NaN, left.m_imaginary / right); 260return new Complex<T>(left.m_real / right, left.m_imaginary / right); 268T d = right.m_imaginary; 285return T.Hypot(value.m_real, value.m_imaginary); 316return new Complex<T>(value.m_real, -value.m_imaginary); 322if (value.m_real == T.Zero && value.m_imaginary == T.Zero) 331return left.m_real == right.m_real && left.m_imaginary == right.m_imaginary; 336return left.m_real != right.m_real || left.m_imaginary != right.m_imaginary; 346return m_real.Equals(value.m_real) && m_imaginary.Equals(value.m_imaginary); 349public override int GetHashCode() => HashCode.Combine(m_real, m_imaginary); 364handler.AppendFormatted(m_imaginary, format); 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); 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)); 447T y2 = two * value.m_imaginary; 450if (T.Abs(value.m_imaginary) <= T.CreateChecked(4)) 465Complex<T> tan = Tan(new Complex<T>(-value.m_imaginary, value.m_real)); 466return new Complex<T>(tan.m_imaginary, -tan.m_real); 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); 566return new Complex<T>(T.Log(Abs(value)), T.Atan2(value.m_imaginary, value.m_real)); 583return FromPolarCoordinates(expReal, value.m_imaginary); 591if (T.IsInfinity(value.m_imaginary)) 593return new Complex<T>(T.PositiveInfinity, value.m_imaginary); 597if (T.IsNaN(value.m_imaginary)) 610if (value.m_imaginary == T.Zero) 626T imaginaryCopy = value.m_imaginary; 629if (T.IsInfinity(value.m_imaginary)) 679T valueImaginary = value.m_imaginary; 681T powerImaginary = power.m_imaginary; 700T imaginaryResult = factor * value.m_imaginary; 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); 829return (value.m_imaginary == T.Zero) && T.IsNegative(value.m_real); 838return (value.m_imaginary == T.Zero) && T.IsNegativeInfinity(value.m_real); 848&& ((value.m_imaginary == T.Zero) || T.IsNormal(value.m_imaginary)); 852public static bool IsOddInteger(Complex<T> value) => (value.m_imaginary == T.Zero) && T.IsOddInteger(value.m_real); 860return (value.m_imaginary == T.Zero) && T.IsPositive(value.m_real); 869return (value.m_imaginary == T.Zero) && T.IsPositiveInfinity(value.m_real); 873public static bool IsRealNumber(Complex<T> value) => (value.m_imaginary == T.Zero) && T.IsRealNumber(value.m_real); 881return T.IsSubnormal(value.m_real) || T.IsSubnormal(value.m_imaginary); 885static bool INumberBase<Complex<T>>.IsZero(Complex<T> value) => (value.m_real == T.Zero) && (value.m_imaginary == T.Zero); 925if (T.IsNegative(y.m_imaginary)) 941else if (T.IsNegative(y.m_imaginary)) 981if (T.IsNegative(y.m_imaginary)) 997else if (T.IsNegative(y.m_imaginary)) 1042if (T.IsNegative(y.m_imaginary)) 1058else if (T.IsNegative(y.m_imaginary)) 1102if (T.IsNegative(y.m_imaginary)) 1118else if (T.IsNegative(y.m_imaginary)) 1148result_realpart = T.MultiplyAddEstimate(-left.m_imaginary, right.m_imaginary, result_realpart); 1151T result_imaginarypart = addend.m_imaginary; 1152result_imaginarypart = T.MultiplyAddEstimate(left.m_real, right.m_imaginary, result_imaginarypart); 1153result_imaginarypart = T.MultiplyAddEstimate(left.m_imaginary, right.m_real, result_imaginarypart); 1351result = (TOther)(object)((value.m_imaginary != T.Zero) ? T.NaN : value.m_real); 1357result = (TOther)(object)new Complex(double.CreateChecked(value.m_real), double.CreateChecked(value.m_imaginary)); 1363if (value.m_imaginary != T.Zero) 1375if (value.m_imaginary != T.Zero) 1403result = (TOther)(object)new Complex(double.CreateSaturating(value.m_real), double.CreateSaturating(value.m_imaginary)); 1434result = (TOther)(object)new Complex(double.CreateTruncating(value.m_real), double.CreateTruncating(value.m_imaginary)); 1647? m_imaginary.TryFormat(Unsafe.BitCast<Span<TChar>, Span<byte>>(destination.Slice(2)), out int imaginaryChars, format, provider) 1648: m_imaginary.TryFormat(Unsafe.BitCast<Span<TChar>, Span<char>>(destination.Slice(2)), out imaginaryChars, format, provider))