w=cos(theta) + isin(theta) where theta is between 0 and pi.
if complex number w^2 + (5/w) -2 is purely imaginary, show that 2(cos^2)(theta) + 5cos(theta) -3=0.
Hence, find w.

w was found to equal (1/2) + ((sqrt3)/2) i
I now know A and B are two points on an Argand diagram representing two distinct non zero complex numbers.
z_2 = w(z_1) where w is stated as above.

i found out the following:
modulus of (z2/z1) equals 1
Arg (z2/z1) equals pi/3

if o is the origin, what type of triangle is OAB?
im guessing the modulus and arg which were asked to be found are revelant somehow. also, am i to assume that A and B are z1 and z2 respectively? otherwise im stuck and the question doesnt clarify.