see here

For two complex numbers and we wish to geometrically interpret .B) Give the geometrical representation of the product of the two complex numbers.

This is probably easier to visualize if you write the complex numbers in polar form, but just to describe it to you. This is taken from Bak's Complex Analysis: "If we form a triangle with two sides given by the vectors (originating from 0 to) 1 and and then form a similar triangle with the same orientation and the vector corresponding to the vector 1, the vector which corresponds to will be ."

write so that . recall thatc) if zz' - 5iz = 10 - 20i , find the possible values of z.

Thus we have

Now expand the brackets on the left, equate coefficients and solve the resulting system of equations to find and and hence,