IMSL C# Numerical Library

Complex.Log Method 

Returns the logarithm of a Complex z, with a branch cut along the negative real axis.

public static Complex Log(
   Complex z
);

Parameters

z
A Complex object.

Return Value

A newly constructed Complex initialized to the logarithm of the argument. Its imaginary part is in the interval [-i\pi,i\pi].

Remarks

Specifically, if z = x+iy,

\log(\bar{z}) = \overline{\log(z)}.

\log(0 + i0) returns - \infty + i\pi.

\log(+0 + i0) returns - \infty + i0.

\log(-\infty + i \infty ) returns + \infty + i3 \pi/4.

\log(+\infty + i \infty ) returns + \infty + i \pi/4.

\log(x + i \infty ) returns + \infty + i \pi/2, for finite x.

\log(-\infty + iy) returns + \infty + i \pi, for finite positive-signed y.

\log(+\infty + iy) returns + \infty + i0, for finite positive-signed y.

\log(\pm \infty + i\NaN) returns + \infty + i\NaN.

\log(\NaN + i \infty ) returns + \infty + i\NaN.

\log(x + i\NaN) returns \NaN + i\NaN, for finite x.

\log(\NaN + iy) returns \NaN + i\NaN, for finite y.

\log(\NaN + i\NaN) returns \NaN + i\NaN.

See Also

Complex Class | Imsl.Math Namespace