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Finding modulus and argument of a complex number

  1. Jan 14, 2009 #1
    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!
  2. jcsd
  3. Jan 14, 2009 #2


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    Science Advisor
    Homework Helper

    Hi choob! :smile:

    You need to learn your trigonometric identities …

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

    and 1 - cos = 2 sin21/2 :wink:
  4. Jan 14, 2009 #3
    i can get arg(z) to arctan(-cos(a/2)/(sin a/2)), how do i finish this?
  5. Jan 14, 2009 #4


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    Homework Helper

    This will help you.

    [tex]tan(\frac{\pi}{2}-\theta)= \frac{1}{tan\theta}[/tex]
  6. Jan 14, 2009 #5
    wow thanks a lot, lol.
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