# Complex Numbers

1. Oct 7, 2007

### dashkin111

[SOLVED] Complex Numbers

1. The problem statement, all variables and given/known data

I was given an equation with complex numbers, and told to convert to polar coordinates. I was able to find r relatively easily, but finding the angle is giving me trouble- I am having difficulties in breaking the equation down into imaginary and real parts.

The equation:

$$\frac{-6}{9+4i}$$

2. Relevant equations

See part 1.

3. The attempt at a solution

I found r by doing the following:

$$\frac{|-6|}{|9+4i|}$$

$$\frac{6}{\sqrt{81+16}}$$

$$r=\frac{6}{\sqrt{97}}$$

Now finding theta is where I get into trouble. I can't seem to understand what to do. I tried just doing it as if all of the fraction was imaginary, which would give me -pi/2 (am I right in thinking this?), but that doesn't work.

Last edited: Oct 7, 2007
2. Oct 7, 2007

### ptr

Attempt to multiply the number by $$\frac{9-4i}{9-4i}$$. Then you can easily separate the real and imaginary parts.

3. Oct 7, 2007

### dashkin111

Ahh wow thank you, I didn't even think of multiplying by the conjugate

It's been years since I did complex numbers so I felt silly asking that, but thank you so much

4. Oct 7, 2007

### Mindscrape

Did you get (6/Sqrt[97])e^(i*156º)?

Last edited: Oct 7, 2007
5. Oct 7, 2007