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

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<div style="font-size:30px">'''IMSQRT(z)'''</div><br/> | <div style="font-size:30px">'''IMSQRT(z)'''</div><br/> | ||

− | *<math> | + | *<math> complex number </math> is of the form <math>z=x+iy</math> |

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*where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> | *where <math>r</math> is the modulus of <math>z</math>. <math>r=\sqrt{x^2+y^2}</math> | ||

*And <math>\theta</math> is the argument of <math>z</math>. <math> θ=tan^{-1}(y/x)</math> also <math>θ∈(-\pi,\pi]</math>. | *And <math>\theta</math> is the argument of <math>z</math>. <math> θ=tan^{-1}(y/x)</math> also <math>θ∈(-\pi,\pi]</math>. | ||

− | *We can use COMPLEX function to convert real and imaginary number in to a complex number. | + | *We can use [[Manuals/calci/COMPLEX| 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 <math>IMSQRT(Complexnumber)</math>. | ||

+ | **<math> complex number </math> is of the form <math>z=x+iy</math> | ||

+ | *For e.g.,IMSQRT("9+10i") | ||

+ | *IMSQRT(IMSUB("9+10i","-2-3i")) | ||

==Examples== | ==Examples== |

## Revision as of 00:26, 26 June 2014

**IMSQRT(z)**

- 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

## See Also