Complex numbers cannot be shown on the number lines studied so far. e.g. Real number line.
Complex numbers can be shown on the complex number plane known as an Argand diagram.
Each number is represented by a point.
The real part is plotted on the horizontal axis and the imaginary part on the vertical axis.
Example
Show the following complex numbers on an Argand diagram.
a = 4 − i , b = 3 + 3i , c = -3 + 2i and d = -4 − 2i
Addition and Subtraction of Complex Numbers on an Argand Diagram
Addition and subtraction of complex numbers can be illustrated on an Argand diagram.
| Let a = 1 + 4i and b = 4 + i | |
| a + b = (1 + 4i) + (4 + i) = 5 + 5i | a − b = (1 + 4i) -(4 + i) = -3 + 3i |
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Notice how the resultant from addition is formed using a parallelogram. Subtraction is drawn by adding the negaitve complex number (-b). |
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