11-2

Hope everyone had a good Thanksgiving holiday :)
So the week before the holidays we learned polar and rectangular:

-Complex numbers are in the form of z=x+y; h rectangular
-In polar complex numbers are in the form of z=rcos(theta)+rsin(theta)
-This is abbrevated as z=rcis(theta)
-Absolute value of z=square root of x^2+y^2
-To multiply complex numbers
1. Rectangular, FOIL *i^2= -1
2. Polar, multiply r and add theta

Example 1:
-1+i
r= square root of (-1)^2 + i^2
= square root of 1+1
= + or - square root of 2

theta= tan inverse of 1 is square root of -1 over -1 = tan 45
negative in the second and fourth: 135 and 315
z= square root of 2cis135

Example 2:
6cis100
y=6sin100 x=6cos100
y=5.909 x=-1.042
z=-1.042+5.909i

--Danielle :)