Review of 11-2

So this week I am going to do my blog on a review of section 11-2. This section is on problems with complex numbers. This should be very simple and easy to remember. So I'll get started by giving you a few formulas.

• 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.

okay, so now I'll do an example for you. I might even do two examples, but it depends.

Example: -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

so, that's it for this week. Hope I helped you remember how to work these problems. byee.

--Halie!