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Finding modulus and argument of a complex number

by choob
Tags: argument, complex, modulus, number
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choob
#1
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
mod(z)=sqrt(a^2+b^2)

3. The attempt at a solution
mod(z)=sqrt((1-cos(a))^2+(-sin(a))^2)
=sqrt(2-2cos(a))

arg(z)=arctan((-sin(a))/(1-cos(a)))

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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tiny-tim
#2
Jan14-09, 06:00 PM
Sci Advisor
HW Helper
Thanks
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
choob
#3
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?

rock.freak667
#4
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]
choob
#5
Jan14-09, 08:19 PM
P: 32
wow thanks a lot, lol.


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