De Moivre's Theorem Exercise

1 Use De Moivre's Theorem to find these powers. Express each argument in the range -π < θ ≤ π
a. (2 cis 0.5) 2 b.( 2 cis )4 c. (3 cis )2 d. (5 cis )4

2 Find the required roots to solve the following equations and show on an Argand diagram.
a. z3 = 8 cis  b. z4 = 9 cis  c. z5 = 32 cis π d. z6 = 125 cis π
3 Change these complex numbers to polar form, use De Moivre's Theorem, and leave in rectangular form:
a. (1 + i)4 b. (√3 + i)5 c. (4 − 2i)6 d. (1 + √3i)3
4 Solve the following equations:

a. z4 = 25

 b. z3 = -8 c. z4 = -100 d. z3 = -27