SOLUTION: show that the complex numbers have square roots and that the square roots are contained in the complex plane.What are the square roots of i?

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: show that the complex numbers have square roots and that the square roots are contained in the complex plane.What are the square roots of i?      Log On


   

Question 899329: show that the complex numbers have square roots and that the square roots are contained in the complex plane.What are the square roots of i?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Using DeMoivre's formula,
sqrt%28i%29=%28cos%2890%29%2Bisin%2890%29%29%5E%281%2F2%29
%280%2Bi%29%5E%281%2F2%29=cos%2890%2F2%29%2Bisin%2890%2F2%29
%280%2Bi%29%5E%281%2F2%29=cos%2845%29%2Bisin%2845%29
%280%2Bi%29%5E%281%2F2%29=sqrt%282%29%2F2%2B%28sqrt%282%29%2F2%29i