Difference between revisions of "Manuals/calci/IMSQRT"

Revision as of 22:12, 18 December 2013

IMSQRT(z)

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 . $i=sqrt(-1)$ .
The square root of a complex number is defined by Failed to parse (syntax error): {\displaystyle \sqrt(z)=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt(r)(cosfrac{θ,2}+isinfrac{θ/2})} ,where r is the modulus of z. $r={\sqrt {x^{2}+y^{2}}}$ and θ is the argument of z.Failed to parse (syntax error): {\displaystyle θ=tan^-1frac{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.

Remarks

Examples

''''''' ''''

Description

This function calculates the square root of a complex number in a + bi or a + bj text format.

IMSQRT

The square root of a complex number is:

IMSQRT(IN)

where IN is the complex number

Let's see an example

I.e =IMSQRT(“2+i”) is 1.4553+0.34356i

@@ Line 8: / Line 8: @@
 *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 .<math>i=sqrt(-1)</math>.
-*The square root of a complex number is defined by  <math>\sqrt(z)=\sqrt{x+iy}=\sqrt{r.e^iθ}=sqrt(r)[cos(θ/2)+isin(θ/2)]</math>,where r is the modulus of z.<math>r=\sqrt(x^2+y^2)</math> and θ is the argument of z.<math> θ=tan^-1(y/x)</math> also <math>θ∈(-Pi(),Pi()].</math>
+*The square root of a complex number is defined by  <math>\sqrt(z)=\sqrt{x+iy}=\sqrt{r.e^iθ}=\sqrt(r)(cosfrac{θ,2}+isinfrac{θ/2})</math>,where r is the modulus of z.<math>r=\sqrt{x^2+y^2}</math> and θ is the argument of z.<math> θ=tan^-1frac{y/x}</math> also <math>θ∈(-Pi(),Pi()].</math>
 *We can use COMPLEX function to convert real and imaginary number in to a complex number.
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