Solving Complex Numbers Equations in Polar Coordinates

[dashkin111]

[SOLVED] Complex Numbers

Homework Statement

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:

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

Homework Equations

See part 1.

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.

 

[ptr]

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

 

[dashkin111]

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

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

 

[Mindscrape]

Did you get (6/Sqrt[97])e^(i*156º)?

 

[dashkin111]

Did you get (6/Sqrt[97])e^(i*156º)?

2.723368 radians