11-4

Easiest lesson..longest problems..

Formula: n square root of z= z^1/n cis (theta/n + k times 360/n)
k= 1, 1, 2, , n-1

Example 1: The cube root of 8i
0+8i
r= square root of 0^2+8^2
= plus of minus square root of 8

theta= tan inverse 8/0 = undefined
= 90 and 270

3 square root of z= 8cis90
z1/3=8 1/3cis(90/3 + 0 times 360/3)
z1/3=8 1/3cis(90/3+ 1 times 360/3)
z1/3=8 1/3cis(90/3+ 2 times 360/3)

z1/3=2cis(30)
z1/3=2cis(150)
z1/3=2cis(270)

Hope everyone had a great holiday! Kayla :)