Difference between revisions of "Manuals/calci/IMSQRT"

Revision as of 14:55, 18 July 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 1: / Line 1: @@
-<div style="font-size:30px">'''IMSQRT(Complexnumber)'''</div><br/>
+<div style="font-size:30px">'''IMSQRT (ComplexNumber)'''</div><br/>
-*<math> complex number </math> is of the form <math>z=x+iy</math>
+*<math>ComplexNumber </math> is of the form <math>z=x+iy</math>
 ==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".
+*IMSQRT(ComplexNumber), where  complex number is in the form of "x+iy".
 *where x&y are the real numbers.<math>i</math> imaginary unit .<math>i=\sqrt{-1}</math>.
+*Consider the complex number z.
 *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{\theta}{2})+isin(\frac{\theta}{2})}</math>
@@ Line 13: / Line 14: @@
 ==ZOS==
-*The syntax is to calculate square root of a complex number in ZOS is <math>IMSQRT(Complexnumber)</math>.
+*The syntax is to calculate square root of a complex number in ZOS is <math>IMSQRT(ComplexNumber)</math>.
-**<math> complex number </math> is of the form <math>z=x+iy</math>
+**<math>ComplexNumber</math> is of the form <math>z=x+iy</math>
 *For e.g.,IMSQRT("9+10i")
 *IMSQRT(IMSUB("9+10i","-2-3i"))