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

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*IMSQRT(z), Where z is the complex number is in the form of "x+iy". | *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 .<math>i=\sqrt{-1}</math>. | *where x&y are the real numbers.'i' imaginary unit .<math>i=\sqrt{-1}</math>. | ||

− | *The square root of a complex number is defined by <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt | + | *The square root of a complex number is defined by <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt{r}(cos(θ/2)+isin(θ/2)</math> |

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

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

*We can use COMPLEX function to convert real and imaginary number in to a complex number. | *We can use COMPLEX function to convert real and imaginary number in to a complex number. |

## Revision as of 23:18, 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.

Remarks

Examples

**'''''''**

**''''**Description

This function calculates the square root of a complex number in a + bi or a + bj text format.

**IMSQRT**

The square root of a complex number is:

**IMSQRT**(**IN**)

where IN is the complex number

Column1 | Column2 | Column3 | Column4 | |

Row1 | 1.455346690225355+0.34356074972251243i | |||

Row2 | ||||

Row3 | ||||

Row4 | ||||

Row5 | ||||

Row6 |

Let's see an example

I.e =IMSQRT(“2+i”) is 1.4553+0.34356i