The points A and B in the complex plane correspond to complex nos. z1 and z2 respectively. Both triangle OAP and OBQ are right angled isosceles triangles.
i) Explain why P correspond to (1+i)z1: Done
ii) M is midpoint of PQ, what complex no. correspond to M
Here is my attempt, which conflict with solutions
Q reqpresents z2(1-i), by rotation.
Since M is mid point of QP, then QM = 1/2 (p-q)
=1/2(z1-z2) + i/2 (z1+ z2)
But QM = M - z2
z2 + QM = M
M = 1/2 ((z1+z2) + i(z1 + z2))
However solutions has 1/2(z1+z2 + i(z1-z2))
Thanks in advance.