1. ## Complex Analysis Geometry

Can someone help me with this following question which I have a lot of trouble with?

Thanks!

The aim of this question is to describe, given two complex numbers representing two vertices of a square, how to find two complex numbers representing the other two vertices of the square.

(a) Show carefully, that if z represents the point on the complex
plane then represents a point with and perpendicular to .

(b) If the given complex numbers and represent two adjacent vertices of the square, there are two possibilities for the pair of
complex numbers representing the other two vertices. What are
they? (And, of course, give a careful justification).

(c) If the given complex numbers and represent two diagonally opposite vertices of the square what is the pair of complex numbers
representing the other two vertices?

2. Originally Posted by lpd
Can someone help me with this following question which I have a lot of trouble with? The aim of this question is to describe, given two complex numbers representing two vertices of a square, how to find two complex numbers representing the other two vertices of the square.
(a) Show carefully, that if z represents the point on the complex plane then represents a point with and perpendicular to .
The first part of part a) is $\left| {iz} \right| = \left| i \right|\left| z \right| = \left| z \right|$

Then note that multiplying by $i$ rotates $z$ by $\frac{\pi}{2}$. So they are perpendicular.