# Manuals/calci/IMSQRT

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 $\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt{r}(cos(θ/2)+isin(θ/2)$
• where r is the modulus of z.
• And θ is the argument of z. $\displaystyle θ=tan^{-1}(y/x)$ 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

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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