Geometric Representation of Complex Numbers

I almost forgot to do my blog tonight, but my bestttfriennddd Danielle reminded me :-)

*Complex numbers are in the form of z=x+yi in rectangular form.
*Complex numbers are in the form of z=rcos(theta)+rsin(theta)i in polar form.
**Remember that i=square root of -1 and cannot be simplified.

***e^ipi=-1

*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:
Express each complex number in polar form. Give angle measures to the nearest degree when necessary.
-1+i
r=square root of -1^2+i^2
r=square root of 1+1(i^2=1)
r=+/-square root of 2
theta=tan^-1(square root of -1/-1)=1=45degrees
theta=135degrees and 315degrees
z=+/-square root of 2cis135degrees
z=+/-square root of 2cis315degrees
z=+/-square root of 2cos315degrees+square root of 2sin315degrees

Example 2:
Express each complex number in polar form. Give angle measures to the nearest degree when necessary.
1+isquare root of 3
r=square root of1^2+isquare root of 3^2
r=square root of 1+3
r=square root of 4
r=+/-2
theta=tan^-1(square root of 3/1)=60degrees
theta=60degrees and 240degrees
z=2cis60degrees
z=2cis240degrees
z=+/-2cos240degrees+2sin240degrees

Example 3:
Express each complex number in rectangular form.
(5cis30degrees)(2cis60degrees)
5(2)=10
60+30=90
10cis90degrees
x=10cos90degrees
y=10sin90degrees
x=0
y=10
0+10i=10i