Difference between revisions of "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 is the modulus of .
• And is the argument of . $\displaystyle θ=tan^{-1}(y/x)$ also θ∈(-Pi(),Pi()].
• We can use COMPLEX function to convert real and imaginary number in to a complex number.

Examples

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