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

by iampaul
Tags: complex, form, number, principal
 P: 79 z= (10-j+elogj)2 I tried expanding but it just made it more complicated. help please!!
 P: 79 the principal form is defined in my book as ln(z)=ln(r)+jθ
HW Helper
P: 6,187
 Quote by iampaul z= (10-j+elogj)2 I tried expanding but it just made it more complicated. help please!!
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?

 P: 79 How do i find the principal form of this complex number 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?
 HW Helper P: 6,187 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?
 P: 79 thanks!!

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