give me some difficult questions on complex numbers

Dear student

Solve these ques:

1)Calculate all integers n such that z_n = (1 + i sqrt(3))ⁿ is a real number.

2)Given: z not real and |z|= 1

               z-1
Show that w =  ---  is a pure imaginary number.
               z+1

Approved

is the answer x=100?? if yes pls approv otherwise pls tell the answer..

Q) Let P(expiθ1) , Q(expiθ2) and R(expiθ3) be the vertices of a triangle PQR in the argand plane. The orthocenter of the triangle PQR is ?

A) expi(θ1+θ2+θ3)               B) 2/3expi(θ1+θ2+θ3)           C)expiθ1+expiθ2+expiθ3          D)none of these 

Approved