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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

Chapter Closure

Exercise 113 Page 365

<listcircle icon="a"> We can simplify the given expression by combining like terms. This involves treating the imaginary unit i as though it was a variable. (3+4i)+(7-2i) Remove parentheses 3+4i+7-2i Commutative Property of Addition 3+7+4i-2i Add terms 10+2i </deduct>

b We can simplify the given expression by combining like terms. This involves treating the imaginary unit i as though it was a variable.

(3+5i)^2

PowToProdTwoFac

a^2=a* a

(3+5i)(3+5i)

Multiply parentheses

3 * 3 + 3 * 5i + 5i * 3 + 5i * 5i

Multiply

9+15i+15i+5i^2

i^2=- 1

9+15i+15i+5(-1)

a(- b)=- a * b

9+15i+15i-5

CommutativePropAdd

Commutative Property of Addition

9-5+15i+15i

Add terms

4+30i

c We can simplify the given expression by combining like terms. This involves treating the imaginary unit i as though it was a variable.

(7+i)(7-i)

Multiply parentheses

7 * 7 - 7 * i + i * 7 + i * (- i)

Multiply

49-7i+7i+i(- i)

a(- b)=- a * b

49-7i+7i-i^2

i^2=- 1

49-7i+7i-(-1)

a-(- b)=a+b

49-7i+7i+1

CommutativePropAdd

Commutative Property of Addition

49+1-7i+7i

Add and subtract terms

50

d We can simplify the given expression by combining like terms. This involves treating the imaginary unit i as though it was a variable.

(3i)(2i)^2

(a * b)^m=a^m* b^m

(3i)(2^2 i^2)

Calculate power

(3i)(4 i^2)

i^2=- 1

(3i)(4(-1))

a(- b)=- a * b

(3i)(-4)

a(- b)=- a * b

-12i

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