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Multiplication of Complex Numbers: Example 7
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Simplify u = (2 – 3i)
2
+ (2 – 3i).
Help on
Complex Numbers
General Contents
Detailed Contents
Index
The "square" term looks like
(a – b)
2
= a
2
– 2ab + b
2
.
What did we call this special product?
We called it "the perfect square of a difference".
Can we use that here?
Yes.
Evaluate the square term using this special product.
(2 – 3i)
2
= 2
2
– 2(2)(3)i + 3
2
(i)
2
, or
(2 – 3i)
2
= 4 – 12i +9i
2
, or
(2 – 3i)
2
= 4 – 12i + 9(–1)
(2 – 3i)
2
= –5 – 12i
Use this to evaluate u (defined in the original problem).
u = –5 –12i + (2 – 3i)
Combine the like terms.
u = –5 + 2 –12i –3i, or
u = –3 –15i.
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