1. What is the smallest positive integer value of n such that (sqrt3/2 - i/2)^n is real?

2. If x + x^-1 = sqrt2, find x^20

3. let z = 3[cos(85) + i*sin(85)]. Find the smallest positive value of r such that r[cos(45) + i*sin(45)] = z^n for some positive integer n.

Guest Dec 26, 2022