Difference between revisions of "Manuals/calci/IMPOWER"

Latest revision as of 04:02, 2 November 2020

IMPOWER(Complexnumber,n)

$Complexnumber$ is of the form $z=x+iy$
is the power value.
- IMPOWER(), returns a complex number raised to an integer power.

This function gives the value of powers of complex number.
DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.
$i$ is the imaginary unit, $i={\sqrt {-1}}$
Then the power of a complex number is defined by

(z)^{n}=(x+iy)^{n}=r^{n}*e^{in\theta }=r^{n}(cosn\theta +isinn\theta )

where $r={\sqrt {x^{2}+y^{2}}}$ and $\theta =tan^{-1}({\frac {y}{x}})$ , $\theta \in (-\pi ,\pi ]$ .

This formula is called DeMoivre's theorem of complex numbers.
We can use COMPLEX function to convert real and imaginary number in to a complex number.
In IMPOWER(Complexnumber,n), $n$ can be integer, fractional or negative.
If $n$ is non-numeric, function will return error value.

The syntax is to calculate powers of Complex number in ZOS is .
- $Complexnumber$ is of the form $z=x+iy$
- $n$ is the power value.
For e.g.,IMPOWER("7-8i",6)

Impower

@@ Line 2: / Line 2: @@
 *<math>Complexnumber</math>  is of the form <math>z=x+iy</math>
 *<math>n</math> is the power value.
+**IMPOWER(), returns a complex number raised to an integer power.
 ==Description==
@@ Line 9: / Line 10: @@
 *Then the power of a complex number is defined by
 :<math>(z)^n=(x+iy)^n=r^n*e^{in\theta}=r^n(cosn\theta+isinn\theta)</math>
-where <math>r=\sqrt{x^2+y^2}</math> and  <math>\theta=tan^{-1}(\frac{y}{x})</math>, <math>\theta∈(-\pi,\pi]</math>.
+where <math>r=\sqrt{x^2+y^2}</math> and  <math>\theta=tan^{-1}(\frac{y}{x})</math>, <math>\theta \isin (-\pi,\pi]</math>.
 *This formula is called DeMoivre's theorem of complex numbers.
 *We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number.
@@ Line 19: / Line 20: @@
 **<math>Complexnumber</math>  is of the form <math>z=x+iy</math>
 **<math>n</math> is the power value.
-*For e.g.,impower("7-8i",6)
+*For e.g.,IMPOWER("7-8i",6)
 {{#ev:youtube|QRkmmsadQhA|280|center|Impower}}
@@ Line 26: / Line 27: @@
 #=IMPOWER("4+5i",3) = -235.99999+115i
 #=IMPOWER("9-7i",4) = -14852-8063.999999i
-#=IMPOWER("6",9) = 10077696
+#=IMPOWER("6",9) = 10077696+0i
-#=IMPOWER("i",10) = -1+6.1257422745431E-16i
+#=IMPOWER("i",10) = -1+0i
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