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.. Done. The answer is $\displaystyle 6\sqrt{2}$.

a)

i. Find |(1 + i)z|

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 a^{2}+ b^{2}= c^{2}?

b) Let z_{1}and z_{2}be non-zero complex numbers satisfying z_{1}^{2 }- 2z_{1}z_{2}+ 2z_{2}^{2}= 0.

If z_{1}= $\alpha$ z_{2}:

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 zHow would I go about doing this?_{1}and z_{2}.