Let z be a complex number with |z| = 6. Let A be the point representing z. Let B be the point representing (1 + i)z.
i. Find |(1 + i)z|. Done. The answer is .
ii. Find |(1 + i)z - z|. Done. The answer is 6.
iii. Prove that OAB is an isosceles right-angled triangle. Is this just a matter of a2 + b2 = c2?
b) Let z1 and z2 be non-zero complex numbers satisfying z12 - 2z1z2 + 2z22 = 0.
If z1 = $\alpha$ z2:
i) show that $\alpha$ = 1 + i or 1 - i. Done.
ii) for each of these values of $\alpha$ describe the geometrical nature of the triangle whose vertices are the origin and the points representing z1 and z2. How would I go about doing this?