Difference between revisions of "Manuals/calci/IMSQRT"

Revision as of 22:40, 25 December 2013

IMSQRT(z)

Failed to parse (syntax error): {\displaystyle \sqrt{z}=\sqrt{x+iy}=\sqrt{r.e^{i\theta}}=\sqrt{{r}cos(\frac{θ}{2})+isin(\frac{θ}{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 (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle θ∈(-pi(),pi()]} .
We can use COMPLEX function to convert real and imaginary number in to a complex number.

@@ Line 9: / Line 9: @@
 *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{θ}{2})+isin(\frac{θ}{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>.