The real number a is called the real part of the complex number z . The complex number bi is called the imaginary part of the complex number z .
Proposition Let z be a complex number.
Then the product is always a real number. A real number can be represented graphically as a point on a number line. For example, the numbers 1, 2.5 and 0.7 can be represented by the points, Complex numbers can be thought of as pairs of real numbers. An elegant way of combining two number lines is to draw them at right angles, forming a plane. When complex numbers are represented as points on a plane with the ' a ' plotted along the horizontal axis, and the ' b ' plotted up the vertical axis, the plane is usually called the complex plane .