11-2

This week I am going to explain how to work problems in 11-2, which are problems using complex numbers. There are a few formulas in this section. These formulas are:

• z=x+yi
• z=rcos theta + rsin theta i
• z=rcis theta
• |z|=square root of x^2 + y^2

Note: To multiply complex numbers:

• With rectangular problems remember to always foil.
• With polar problems you will multiply r and add theta.

Now I am going to do a few examples to help you understand how to work these problems.

Example 1: -1 + i

• Since it is in rectangular form, you are going to find r and theta.
• r=square root of -1^2 + 1^2. Which equals square root of 2.
• theta=tan^-1(-1). Which equals 45.
• When you put that on the quadrants, you will get 135 and 315.
• So once you do that, your answers will be square root of 2 cis 135 degrees and -square root of 2 cis 315 degrees.

Example 2: 6 cis 100 degrees

• x=6 cos 100= -1.042
• y=6 sin 100= 5.909
• Your answer is going to be -1.042 + 5.909

Well, that is all for this week. BYEEE

--Halie