Related Function:

The IMSQRT function returns the square root of a complex number in x + yi or x + yj text format.

Syntax

=IMSQRT(inumber)

Arguments

Argument Description
inumber A complex number for which you want the square root

Note: Use the COMPLEX function to convert real and imaginary coefficients into a complex number.

Examples

  A B C D
1 Data Formula Result Notes
2 3+4i =IMSQRT(A2)    
3   =IMSQRT(“3+4i”)    
4   =IMSQRT(“2-i”)    
5   =IMSQRT(COMPLEX(4,1))    

Common Function Error(s)

Problem What went wrong
#NUM! Occurs if the supplied inumber argument is not recognized as a complex number
#NAME? Occurs when Analysis ToolPak add-in is not enabled

The square root of a complex number is calculated as:  

    \[    \sqrt{x+yi} = \sqrt{r}\ cos \left( \frac{\theta}2 \right) + i \sqrt{r}\ sin \left( \frac{\theta}2 \right)   \]

    \begin{align*}\text{where: }& r = \sqrt{x^2 + y^2}  \\\text{and: }& \theta = tan^{-1} \left( \frac y{x} \right)  \\\text{and: }& \theta \epsilon (-\pi; \pi] \\\end{align*}

See Wikipedia for more information on complex numbers.