[JCH2CNAGDH_20150402] Vector Rotation via Complex Numbers

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  re^iq  gives a stretching effect, as well as a rotating effect.  The stretch is by  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