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Argand diagrams

  1. May 14, 2007 #1
    1. The problem statement, all variables and given/known data

    If w=costheta + i sintheta and theta is between -pi and pi: Find theta if E O and A are on the same straight line. E is a point on diagram representing w(z3).

    2. Relevant equations

    3. The attempt at a solution

    Ive found the following:
    z1 (1+(sqrt3)i)
    z2 (-2+(2sqrt3)i)
    z3 (-3+(sqrt3)i)

    so.. i substituted w and z3.
    (costheta + i sintheta)(-3+(sqrt3)i) is equal to (-3costheta -(sqrt3)sintheta) + ((sqrt3)costheta - 3sintheta)i

    How can i work with knowing that E O and A are on the same straight line?
    I should be able to find theta if i can be directed from here...

    Attached Files:

    Last edited: May 14, 2007
  2. jcsd
  3. May 14, 2007 #2


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    Homework Helper

    same straight line? I presume that O is the origin and A is the complex number that has an angle of 60 deg in you diagram. So complex number E must have either an argument of 60 or -120. (i hope I understood you diag + symb correctly)
  4. May 14, 2007 #3
    ye same brain waves cos i came back to same angles as urs. its just this part of question is worth 4 marks, i figured thers more to it than that. ah well.
  5. May 14, 2007 #4


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    Homework Helper

    well 1 marks for understanding the question and working out the strategy,
    1 mark for finding angle for A then
    2 marks for actually finding the angle for z3 and then angle for E.
    that sounds about right.
  6. May 14, 2007 #5
    uve got it all figured out. preciate it muchly. that speed one too. which was a popular answer in class. majority rules.
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