Difference between revisions of "Manuals/calci/IMSQRT"

Revision as of 13:08, 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 $z$ . 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.

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 7: / Line 7: @@
 *where x&y are the real numbers.<math>i</math> 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^{i\theta}}=\sqrt{{r}(cos(\frac{θ}{2})+isin(\frac{θ}{2})}</math>
+<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>.