# Difference between revisions of "Manuals/calci/IMSQRT"

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:

$\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}$

• where is the modulus of . • And is the argument of . $\displaystyle θ=tan^{-1}(y/x)$ also $\displaystyle θ∈(-\pi,\pi]$ .
• 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"))
Imaginary Square Root

## Examples

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

IMSQRT