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Pearson Algebra 2 Common Core, 2011
PA
Pearson Algebra 2 Common Core, 2011 View details
End-of-Course Assessment

Exercise 6 Page 964

Use the definition of the the imaginary unit i. Then, simplify the expression by combining like terms.

I

Practice makes perfect

We want to find the product of two complex numbers. (2+5i)(4+3i) To do so, we will begin by distributing one of the terms.

(2+5i)(4+3i)
Distr

Distribute (2+5i)

4(2+5i)+3i(2+5i)
Distr

Distribute 4

8+20i+3i(2+5i)
Distr

Distribute 3i

8+20i+6i+15i^2

Now, we can recall the definition of the imaginary unit i. i^2= -1 We will use this definition into the given expression. Then, we will simplify the result by combining like terms. Let's do it!

8+20i+6i+15i^2
IDefPow

i^2=- 1

8+20i+6i+15(- 1)
MultPosNeg

a(- b)=- a * b

8+20i+6i+(- 15)
AddNeg

a+(- b)=a-b

8+20i+6i-15
AddSubTerms

Add and subtract terms

-7 +26 i

This corresponds to option I.

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