# Homework Help: Help with Complex function

1. Jan 12, 2013

### pistolpete333

Hi, so for a hw problem I have to evaluate these complex functions. The one I am having trouble on is:

evaluate h(z) = Re(z) / Im(z) where z = (5-2i) / (2 - i)

The answer is in the back of the book, which says that the solution is 12, however I keep getting -12i for my answer. I just need someone to tell me where am going wrong.

I first multiply z by (2 + i) / (2 + i) in order to move the imaginary number to the top, which leaves me with (12 + i) / 5, I then take the real part, 12 / 5 , and put it over the imaginary part, i / 5, and simplify this to 12 / i , where I multiply this by i / i , which leaves me with -12i

The answer is supposed to be 12, so if anyone could shed some light on this that would be great. Thanks everyone

2. Jan 12, 2013

### LCKurtz

The imaginary part of 12/5 + (1/5)i is 1/5.

3. Jan 12, 2013

### Ray Vickson

Re(z) and Im(z) are both REAL, so their ratio must be real as well.

4. Jan 12, 2013

### pistolpete333

Wow that was pretty obvious. I knew I was messing something up, thanks guys