Then the second equation becomes . This means either or . These are the answers that were given above. Just as we can plot real numbers as points on a line, we can think of complex numbers as lying on a plane. What is most useful about this visualisation of the complex numbers is how addition and multiplication behave.
Multiplication is a bit more difficult to see.
Before we go on, it is useful to introduce another means of specifying points in the plane. Suppose that X is any point in a plane and suppose that O is the origin. This angle and distance are known as the polar coordinates of X . Multiplication corresponds to adding the angles of the two points and multiplying their lengths. Understanding multiplication helps us understand other operations such as taking the square root.