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## Homework Statement

Find the modulus and argument of z=1-cos(a)-i*sin(a)

## Homework Equations

mod(z)=sqrt(a^2+b^2)

## 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!