Explain how to multiply complex numbers and give an example ?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter1: Equations And Inequalities
Section1.3: Complex Numbers
Problem 112E
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Explain how to multiply complex numbers and give an example ?

Expert Solution
Step 1

Let us consider two complex numbers say - 

Z1=a+ib   and

Z2=x+iy

On multiplying these two complex numbers-

Z1×Z2=a+ibx+iy

Z1×Z2=ax+i(ay)+i(bx)+i2(by)

Z1×Z2=ax+i(ay+bx)+i2(by)

We know i = -1, then

i2=-1×-1=-1

Then,

Z1×Z2=ax+i(ay+bx)-by

Z1×Z2=ax-by+i(ay+bx)

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