**Question**

The points
D
and G in an Argand diagram
represent the complex numbers 3i and
6 + 7i respectively. DG is in fact a diagonal of the square DFGH. Find the complex numbers represented
by F and H. |

**Introduction**

This is a question that tests students’ concept
of the geometry complex numbers. The key
to solving this question is to understand that multiplying a complex number

*r*e^{i}*gives a stretching effect, as well as a rotating effect. The stretch is by*^{q}*r*times and the rotation is by*q*radians anti-clockwise. If*r*= 1, then there is just rotation and effectively no stretching.**Important Principles**

__Solution__
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