# Answer to Question #5106 in Abstract Algebra for Annemarie

Question #5106

(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.

(b) Find the two square roots of 1 + *Square root* 3 i. Express them in polar form.

Expert's answer

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)

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)

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