Finding modulus and argument of a complex number

  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
    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!
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    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. i can get arg(z) to arctan(-cos(a/2)/(sin a/2)), how do i finish this?
     
  5. rock.freak667

    rock.freak667 6,228
    Homework Helper

    This will help you.

    [tex]tan(\frac{\pi}{2}-\theta)= \frac{1}{tan\theta}[/tex]
     
  6. wow thanks a lot, lol.
     
Know someone interested in this topic? Share a link to this question via email, Google+, Twitter, or Facebook

Have something to add?