Core Connections Integrated II, 2015
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Core Connections Integrated II, 2015 View details
2. Section 8.2
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Exercise 43 Page 446

Practice makes perfect
a We want to simplify the given numeric expression using the imaginary number i. To do so, we will first recall that the imaginary unit i is the complex number whose square is - 1.
i^2=- 1 We can simplify the given expression by using the above definition and combining like terms.
(3+2i)(4+i)
â–Ľ
Distribute
(3+2i)4+(3+2i)i
12+8i+(3+2i)i
12+8i+3i+2i^2
12+8i+3i+2(- 1)
12+8i+3i-2
10+11i
b Like in Part A, we want to simplify the given numeric expression using the imaginary number i. To do so, we will first recall that the imaginary unit i is the complex number whose square is - 1.
i^2=- 1 We can simplify the given expression by using the above definition and combining like terms.
(2+3i)(2-3i)
â–Ľ
Distribute
2(2+3i)-3i(2+3i)
4+6i-3i(2+3i)
4+6i-6i-9i^2
4+6i-6i-9(- 1)
4+6i-6i+9
13
c Like in Parts A and B, we want to simplify the given numeric expression using the imaginary number i. To do so, we will first recall that the imaginary unit i is the complex number whose square is - 1.
i^2=- 1 We can simplify the given expression by using the above definition and combining like terms.
(5-2i)(5+2i)
â–Ľ
Distribute
5(5-2i)+2i(5-2i)
25-10i+2i(5-2i)
25-10i+10i-4i^2
25-10i+10i-4(-1)
25-10i+10i+4
29
d Like in previous parts, we want to simplify the given numeric expression using the imaginary number i. To do so, we will first recall that the imaginary unit i is the complex number whose square is - 1.
i^2=- 1 We can simplify the given expression by using the above definition and combining like terms.
(a+bi)(a-bi)
â–Ľ
Distribute
a(a+bi)-bi(a+bi)
a^2+abi-bi(a+bi)
a^2+abi-abi-b^2i^2
a^2+abi-abi-b^2(-1)
a^2+abi-abi+b^2
a^2+b^2