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

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#=IMSQRT("7")=2.64575131106459 | #=IMSQRT("7")=2.64575131106459 | ||

#=IMSQRT("8i")=2+2i | #=IMSQRT("8i")=2+2i | ||

+ | |||

+ | ==See Also== | ||

+ | *[[Manuals/calci/IMREAL | IMREAL ]] | ||

+ | *[[Manuals/calci/IMSUM | IMSUM ]] | ||

+ | *[[Manuals/calci/IMAGINARY | IMAGINARY ]] | ||

+ | *[[Manuals/calci/COMPLEX | COMPLEX ]] | ||

+ | |||

+ | |||

+ | ==References== | ||

+ | [http://en.wikipedia.org/wiki/Binary_logarithm Binary Logarithm] |

## Revision as of 23:30, 18 December 2013

**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 r is the modulus of z.
- And θ is the argument of z.
**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