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(1+i)-z2(1-i))

...

=1/2(z1-z2) + i/2 (z1+ z2)

But QM = M - z2

z2 + QM = M

therefore,

M = 1/2 ((z1+z2) + i(z1 + z2))

However solutions has 1/2(z1+z2 + i(z1-z2))

Thanks in advance.