# Finding modulus and argument of a complex number

by choob
Tags: argument, complex, modulus, number
 P: 33 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!
 PF Patron HW Helper Sci Advisor Thanks P: 25,494 Hi choob! You need to learn your trigonometric identities … in this case, sin = 2 sin1/2 cos1/2 and 1 - cos = 2 sin21/2
 P: 33 i can get arg(z) to arctan(-cos(a/2)/(sin a/2)), how do i finish this?
HW Helper
P: 6,191

## Finding modulus and argument of a complex number

$$tan(\frac{\pi}{2}-\theta)= \frac{1}{tan\theta}$$