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Finding modulus and argument of a complex number

by choob
Tags: argument, complex, modulus, number
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Jan14-09, 05:50 PM
P: 32
1. The problem statement, all variables and given/known data
Find the modulus and argument of z=1-cos(a)-i*sin(a)

2. Relevant equations

3. The attempt at a solution


This is as far as I can get, I have asked my math teacher but he is not very familiar with thise.

my textbook gives mod(z) as 2sin(2a) and arg(z) as (a-pi)2

BTW this question is from the IB math textbook, there exists a solutions manual but I do not have it... the question is 11.2, 19 a)

Thanks in advance!
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Jan14-09, 06:00 PM
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tiny-tim's Avatar
P: 26,157
Hi choob!

You need to learn your trigonometric identities

in this case, sin = 2 sin1/2 cos1/2

and 1 - cos = 2 sin21/2
Jan14-09, 06:47 PM
P: 32
i can get arg(z) to arctan(-cos(a/2)/(sin a/2)), how do i finish this?

Jan14-09, 06:58 PM
HW Helper
P: 6,206
Finding modulus and argument of a complex number

This will help you.

[tex]tan(\frac{\pi}{2}-\theta)= \frac{1}{tan\theta}[/tex]
Jan14-09, 08:19 PM
P: 32
wow thanks a lot, lol.

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