1:

Prove the following:

zw* - z*w is purely imaginary or zero for all complex numbers z and w

2:

A geometric series has a second term of 6 and the sum of its first three terms is -14. Find its fourth term.

3:

Is it possible to bend a 20 cm length of wire into the shape of a rectangle which has an area of 30cm2?

4:

Find the first two terms of an arithmetic sequence where the sixth term is 21 and the sum of the first seventeen terms is 0.