1. Why do we need the set of complex numbers?

One of the most immediate uses is the solution of quadratic equations with negative discriminants.

This means that when the quadratic formula is used the term inside the square root sign, b2 − 4ac, turns out to be negative. Use of the number i allows this problem to be solved.

2. Can complex numbers be shown on a graph?

Yes, Argand diagrams are used to represent complex numbers (covered in topic 38).