January 2014
Intermediate to advanced
144 pages
4h 2m
English
Content preview from Mathematical Formulas for Industrial and Mechanical Engineering
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2.12 The Complex Plane
The geometric representation of complex numbers is to represent the complex
number ðx; yÞ as the point ðx; yÞ.
y-axis
x-axis
(2,–3)
2
1
12
So the real number ðx; 0Þ is the point on the horizontal x-axis, the purely imaginary
number yi 5 ð0; yÞ is on the vertical y-axis. For the complex number ðx; yÞ, x is the real
part and y is the imaginary part. Example: Locate 2 2 3i on the graph above.
How do we divide complex numbers? Let’s introduce the conjugate of a complex
number then go to division.
Given the complex number z 5 x 1 iy, define the conjugate
z 5 x 1 iy 5 x 2 iy.
We can divide by using the following formula:
z
1
z
2
5
x
1
1 iy
1
x
2
1 iy
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