Changes

*This function gives the value of powers of complex number.

*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.

*DeMoivre's Theorem is a generalized formula to compute powers of a complex number in it's polar form.

*i'is the imaginary unit, <math>i=\sqrt{-1}</math>

*<math>i</math> is the imaginary unit, <math>i=\sqrt{-1}</math>

*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(y/x)</math>, <math>\theta∈(-\pi,\pi]</math>.  

*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(y/x)</math>, <math>\theta∈(-\pi,\pi]</math>.  

*This formula is called DeMoivre's theorem of complex numbers.  

*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.  

*We can use [[Manuals/calci/COMPLEX| COMPLEX]] function to convert real and imaginary number in to a complex number.