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Complex number question

  1. Apr 30, 2009 #1
    1. The problem statement, all variables and given/known data

    If z = cis @ where @ is acute, determine the modulus and argument of z-1


    2. Relevant equations



    3. The attempt at a solution

    As the moudlus of z is 1 z lies on the unit circle. And I can not think of anything more. I drew a graph to see how z-1 seems like in graph and stucked.
    Help me please!
     
  2. jcsd
  3. Apr 30, 2009 #2

    dx

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    The modulus of x + iy is √(x² + y²) and the argument is tan-1(y/x). Draw the vector in the complex plane to see why.
     
  4. Apr 30, 2009 #3
    That I know; but this thing is little different from the normal quetions where the number is multiplied to z such as -z, 2z etc which i can use that formula but here i think i should know some angles and shape of graph
    I saw the answer and it was
    moduls = 2 sin (@/2) argument = (@/2) + (pi/2)
     
  5. Apr 30, 2009 #4

    dx

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    It's possible to do using just the formulas I wrote, but it's easier to do pictorially. Look at the attachment:

    http://img99.imageshack.us/img99/86/picqrv.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
  6. Apr 30, 2009 #5
    Wow i also drew some similar graph but couldnt understand what to do with that but by drawing the line at the middle everything become clear.
    Thankyou so much!!!!!!!
     
  7. Apr 30, 2009 #6

    dx

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    No problem.
     
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