# Manuals/calci/IMSQRT

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**IMSQRT(Complexnumber)**

- 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. 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^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}}**

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

## ZOS Section

- The syntax is to calculate square root of a complex number in ZOS is .
- is of the form

- For e.g.,IMSQRT("9+10i")
- IMSQRT(IMSUB("9+10i","-2-3i"))

## Examples

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

## Related Videos

## See Also