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