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Due to their
unique nature, complex numbers cannot be represented on a normal set of
coordinate axes.
In 1806, J. R.
Argand developed a method for displaying complex numbers graphically as a
point in a coordinate plane. His method, called the
Argand diagram, establishes
a relationship between the x-axis (real axis) with real numbers and the
y-axis (imaginary axis) with imaginary numbers.
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In the
Argand diagram, a complex number a
+
bi is the point (a,b) or the
vector from the origin to the point (a,b). |
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Graph the complex
numbers:
1. 3 + 4i
(3,4)
2. 2 - 3i
(2,-3)
3. -4 + 2i
(-4,2)
4. 3
(which is really 3 + 0i)
(3,0)
5. 4i
(which is really 0
+ 4i)
(0,4)
The
complex number is represented by the point, or by the vector
from the origin to the point.
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Add 3 + 4i and -4 + 2i
graphically.
Graph the two
complex numbers 3 + 4i and -4 + 2i as vectors.
Create a parallelogram using these two vectors
as adjacent sides.
The answer to the addition is the vector
forming the diagonal of the parallelogram (read from the
origin). This new vector
is called the resultant vector. |
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Subtract 3 + 4i from -2
+ 2i
Subtraction is the process of
adding the additive inverse.
(-2 + 2i) - (3 + 4i)
= (-2 + 2i) + (-3 - 4i)
= (-5 - 2i)
Graph the two complex numbers
as vectors.
Graph the additive inverse of
the number being subtracted.
Create a parallelogram using
the first number and the additive inverse. The answer is
the vector forming the diagonal of the parallelogram. |
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