# How do i find the principal form of this complex number

1. Dec 14, 2012

### iampaul

z= (10-j+elogj)2

I tried expanding but it just made it more complicated.

2. Dec 14, 2012

### iampaul

the principal form is defined in my book as
ln(z)=ln(r)+jθ

3. Dec 14, 2012

### I like Serena

Hi iampaul!

To find the principal form you need to find the length and the angle of z.
First step is to find the length and angle of 10-j.
And also of elogj.
Do you know how?

4. Dec 15, 2012

### iampaul

How?
That's exactly what my problem is.
10-j and elogj
aren't similar to any of the forms discussed in school.
Can you give another hint?

5. Dec 15, 2012

### I like Serena

Let's try and find ln(z)=ln(r)+jθ for 10-j and for elogj.

ln(10-j) = -j ln(10) = ln(1) - j ln(10)

So what is the length r and what is the angle θ for 10-j?

Let's break elogj apart a little further.

First we look at "j".
Did you know that "j" has length 1 and angle pi/2?
In other words, we have:
$$j = e^{j {\pi \over 2}}$$

Can you take the log of j?

And if so, find the length and angle of elogj?

6. Dec 17, 2012

thanks!!