11-2

Today I'm going to teach 11-2, which involves solving problems using complex numbers. This is a fairly easy section. There are a few formulas. They are:

z = x+yi (in rectangular)

z = rcos(theta)+rsini OR rcis(theta) (in polar)

z = square root of x^2+y^2

Remember that i = square root of -1 and cannot be simplified.

To multiply complex numbers you must: 1. foil (if expressing in rectangular) 2. multiply r and add theta (if expressing in polar)

Now I have examples to help work out these problems.

Example 1: Express in polar form.

3-4i

First we need to find r and theta. This is when the formulas from 11-1 come back.

r = square root of 3^2 + (-4)^2

r = +/- 5

theta = tan^-1((-4)/3)

theta = 307 degrees7'48" , 127 degrees7'48"

Now we have to write it out in polar form. To do this you have to find out which quadrant your original formula falls in. Then that's how you determine which r go with which theta. Since 3,-4 falls in the foruth quadrant so r=5 and theta=307 degrees7'48" goes together. Your answers are:

z=5cis307degrees7'48"

z=-5cis127degrees7'48"

Example 2: Express in rectangular form

6cis100 degrees

In order to do this you have to find x and y first. Once again, formulas from 11-1 are going to be used again.

x = 6cos100 degrees

x = -1.04

y = 6sin100 degrees

y = 5.909

Now you just write the answer like an formula.

z = -1.04 + 5.909

-danaaaa(: