ok..

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.

thanks..