Answer to Question #5106 in Abstract Algebra for Annemarie

Question

(a) Let z =1 + i. What is z100 in both rectangular and polar form?
(b) Find the two square roots of 1 + *Square root* 3 i. Express them in polar form.

Answer 1

a)
Polar form: 2^(50)*E^(i*Pi);
Rectangular form:
-2^(50);


b)
Sqrt(2)*E^(i*Pi/6)
Sqrt(2)*E^(i*7*Pi/6)