Chapter Eleven

This week our class began chapter eleven and learned chapter complex numbers. Complex numbers have two forms : polar and rectangular.

The rectangular form for complex numbers is z= x + yi

The polar form for complex numbers is z= rcos(x)rsin(x)i or it can be abbreviated as z=rcis(x)

In section one we learned how to convert polar to non polar and vice versa.

Rectangular coordinates are formed by ( x,y)

Polar coordinates are in the form of (r,θ)

In order to convert from rectangular to polar you must solve for “r” and theta.
*r=sqrt of x^2+y^2. Theta is equal to tan y/x
You will always have two answers when converting to polar. One positive and one negative.
EX. A (3,3) CONVERT TO POLAR :
R=sqrt 3^2=3^2 = 9+9
R=sqrt18 = ±2√3
Theta= tan y/x
theta= tan(3/3) = tan 1
theta = 45, 225

*(3,3) is located in the first two quadrants therefore the positive number gets the smaller number. Your answers are (2, 45) (-2,225)
In order to convert to rectangular , you simply use formulas x= rcostheta and y=rsintheta