Graph of complex numbers |
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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: |
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| Imaginary Axis |
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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. |
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| Plot the following points on the graph: |
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Example 1 |
A = -2 + 3i
= (-2,3) |
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Example 2 |
B = 3- 4i
=(3, -4) |
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Example 3 |
C = 5 + 6i
= (5,6) |
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Example 4 |
D = 0- 7i
= (0, -7) |
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Example 5 |
E = 4 + 0i
= (4, 0) |
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Example 6 |
F = -1-i
= (-1, -1) |
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| Imaginary Axis |
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Try these questions |
| Plot the following points on the graph. |
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- A = -5 – i
Answer: ( -5, -1)
- B = -7 +4i
Answer: (-7, 4)
- C = 8 -7i
Answer: (8, -7)
- D = -3i
Answer: (0,-3)
- E = -6
Answer: (-6,0)
- F = 2i
Answer: (0,2)
- G = 9
Answer: (9,0)
- H = 3+ 7i
Answer: (3, 7)
- I = -5i + 7
Answer: (7,-5)
- J = -3i - 6.
Answer: (- 6,-3) |
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| Imaginary axis |
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