# Manuals/calci/IMSQRT

**IMSQRT(z)**

- is the complex number is of the form

## Description

- This function gives square root of a complex number.
- IMSQRT(z), Where z is the complex number is in the form of "x+iy".
- where x&y are the real numbers.'i' imaginary unit ..
- The square root of a complex number is defined by:

**Failed to parse (syntax error): {\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt{r}(cos(θ/2)+isin(θ/2)}**

- where is the modulus of .
- And θ is the argument of .
**Failed to parse (syntax error): {\displaystyle θ=tan^{-1}(y/x)}**also θ∈(-Pi(),Pi()]. - We can use COMPLEX function to convert real and imaginary number in to a complex number.

## Examples

- =IMSQRT("2+3i")=1.67414922803554+0.895977476129838i
- =IMSQRT("-4-5i")=1.09615788950152-2.2806933416653i
- =IMSQRT("7")=2.64575131106459
- =IMSQRT("8i")=2+2i

## See Also