Practice Questions – Complex Numbers

Q1. The complex numbers  z1 and  z2 are given by  z1=2+2i and  z2=3i

(i) Find the modulus and argument of each of  z1 and  z2 .  [6 marks]
(ii) Plot the points representing each of z1z2 and  z1+z2 on an Argand diagram. [3 marks]
(iii) Hence find the exact value of  tanπ24 . [5 marks]





Q6. (i) The complex number  z is such that z2=1+i3 . Find the two possible values of  in the forma a+ib , where  a and b are exact real numbers. [5 marks]
(ii) With the value of  z from part (i)such that the real part of z is positive, show on an Argand diagram the points A and B representing  z and z2 respectively. [2 marks]
(iii) Specify two transformations which together map the line segment OA to the line segment OB, where O is the origin. [4 marks]