Returns the square root of a Complex, with a branch cut along the negative real axis.

Namespace: Imsl.Math
Assembly: ImslCS (in ImslCS.dll) Version: 6.5.0.0

Syntax

C#
public static Complex Sqrt( Complex z )

Visual Basic (Declaration)
Public Shared Function Sqrt ( _ z As Complex _ ) As Complex

Visual C++
public: static Complex Sqrt( Complex z )

A newly constructed Complex initialized to square root of z.

Remarks

Specifically, if z = x+iy,

${\rm sqrt}(\bar{z}) = \overline{{\rm sqrt}(z)}$ .

${\rm sqrt}(\pm 0 + i0)$ returns .

${\rm sqrt}(-\infty + iy)$ returns $+0 + i\infty$ , for finite positive-signed y.

${\rm sqrt}(+\infty + iy)$ returns $+ \infty + i0$ , for finite positive-signed y.

${\rm sqrt}(x+i\infty)$ returns $+ \infty + i \infty$ , for all x (including NaN).

${\rm sqrt}(-\infty + i \NaN)$ returns $\NaN \pm i \infty$ (where the sign of the imaginary part of the result is unspecified).

${\rm sqrt}(+\infty + i \NaN)$ returns $+\infty + i \NaN$ .

${\rm sqrt}(x + i \NaN)$ returns $\NaN + i \NaN$ and optionally raises the invalid exception, for finite x.

${\rm sqrt}(\NaN + iy)$ returns $\NaN + i \NaN$ and optionally raises the invalid exception, for finite y.

${\rm sqrt}(\NaN + i \NaN)$ returns $\NaN + i \NaN$ .