# Argand diagrams

1. May 14, 2007

### ahoy hoy

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...

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Last edited: May 14, 2007
2. May 14, 2007

### mjsd

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)

3. May 14, 2007

### ahoy hoy

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.

4. May 14, 2007

### mjsd

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.