Difference between revisions of "Manuals/calci/IMSQRT"

Revision as of 13:09, 21 March 2018

IMSQRT(Complexnumber)

${\sqrt {z}}={\sqrt {x+iy}}={\sqrt {r.e^{i\theta }}}={\sqrt {{r}(cos({\frac {\theta }{2}})+isin({\frac {\theta }{2}})}}$

where $r$ is the modulus of $z$ . $r={\sqrt {x^{2}+y^{2}}}$
And $\theta$ is the argument of $z$ . $\theta =tan^{-1}(y/x)$ also $\theta \in (-\pi ,\pi ]$ .
We can use COMPLEX function to convert real and imaginary number in to a complex number.

The syntax is to calculate square root of a complex number in ZOS is .
- $complexnumber$ is of the form $z=x+iy$
For e.g.,IMSQRT("9+10i")
IMSQRT(IMSUB("9+10i","-2-3i"))

Imaginary Square Root

@@ Line 9: / Line 9: @@
 <math>\sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}(cos(\frac{\theta}{2})+isin(\frac{\theta}{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> \theta=tan^{-1}(y/x)</math> also <math>\theta \isin (-\pi,\pi]</math>.
 *We can use [[Manuals/calci/COMPLEX| COMPLEX]]  function to convert real and imaginary number in to a complex number.