Definition

The entire plane in which each point corresponds to a complex number is called the complex plane or Argand plane. The x – axis is called the real axis the y – axis is called the imaginary axis.

Let the point P represent z, the complex number in the complex plane.

Point P = z = a + ib = (a, b)

P is represented on the graph as follows:

Imaginary Axis

The complex numbers of the form a + i0 = (a, 0) are points on the x-axis.

The complex numbers of the form 0 + ib = (0,b) are points on the y-axis.

The plotted points on the graph are given below.

Plot the following points on the graph:

Example 1

Sketching the graph of the equation y = |x|, we have

A = -2 + 3i

= (-2,3)

Example 2

B = 3- 4i

=(3, -4)

Example 3

C = 5 + 6i

= (5,6)

Example 4

D = 0- 7i

= (0, -7)

Example 5

E = 4 + 0i

= (4, 0)

Example 6

F = -1-i

= (-1, -1)

Imaginary Axis

Real Axis

Try these questions

Plot the following points on the graph.

1. A = -5 – i
   Answer: ( -5, -1)
2. B = -7 +4i
   Answer: (-7, 4)
3. C = 8 -7i
   Answer: (8, -7)
4. D = -3i
   Answer: (0,-3)
5. E = -6
   Answer: (-6,0)
6. F = 2i
   Answer: (0,2)
7. G = 9
   Answer: (9,0)
8. H = 3+ 7i
   Answer: (3, 7)
9. I = -5i + 7
   Answer: (7,-5)
10. J = -3i - 6.
    Answer: (- 6,-3)

Imaginary axis

Real axis