11-3

11-3
Throwing back to Chapter 11.. Section 11-3 was very short and simple. It dealt with De Moivre’s Theorem. There’s just one simple formula for this section:
(r cis theta)^n = r^n cis n theta

EXAMPLE 1: If z=3 cis 10^6, find z^6.
A). z^6 = 3^6 cis 6(10)
B). z^6 = 729 cis 60
Pretty simple right?

EXAMPLE 2: If z=2 cis 4^3, find z^3.
A). z^3 = 2^3 cis 3(4)
B). z^3 = 8 cis 12

This is too short so I’m going to add an example problem from another section of Chapter 11.

EXAMPLE 1: Convert to rectangular – (3, pi)
A). We should all remember our formulas but if not, here they are..
x= r cos theta and y=r sin theta
B). x=3 cos pi and y=3 cos pi
C). According to our unit circle, we know that pi is 180. At 180 degrees cos is -1 (x axis)and sin is 0 (y axis).
D). x=3(-1) and y=3(0)
E). Your answer is the point (-3,0)