Lesson 13
Multiplying Complex Numbers
Problem 1
Which expression is equivalent to \(2i(5+3i)\)?
\(\text-6 + 10i\)
\(6 + 10i\)
\(\text-10 + 6i\)
\(10+ 6i\)
Solution
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Problem 2
Lin says, “When you add or multiply two complex numbers, you will always get an answer you can write in \(a + bi\) form.”
Noah says, “I don’t think so. Here are some exceptions I found:”
\((7 + 2i) + (3 - 2i) = 10\)
\((2 + 2i)(2 + 2i) = 8i\)
- Check Noah’s arithmetic. Is it correct?
- Can Noah’s answers be written in the form \(a+bi\), where \(a\) and \(b\) are real numbers? Explain or show your reasoning.
Solution
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Problem 3
Explain to someone who missed class how you would write \((3-5i)(\text-2+4i)\) in the form \(a+bi\), where \(a\) and \(b\) are real numbers.
Solution
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Problem 4
Which expression is equal to \(729^{\frac23}\)?
243
486
\(9^2\)
\(27^3\)
Solution
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(From Unit 3, Lesson 4.)Problem 5
Find the solution(s) to each equation, or explain why there is no solution.
- \(2x^2-\frac23= 5\frac13\)
- \((x+1)^2=81\)
- \(3x^2+14=12\)
Solution
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(From Unit 3, Lesson 7.)Problem 6
Plot each number in the complex plane.
- \(5i\)
- \(2+4i\)
- -3
- \(1 - 3i\)
- \(\text-5 - 2i\)
Solution
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(From Unit 3, Lesson 11.)Problem 7
Select all the expressions that are equivalent to \((3x+2)(x-4)\) for all real values of \(x\).
\(3x^2-12\)
\(3x^2-10x-8\)
\(3(x^2 + 2x - 4)\)
\(3(x^2-3x)-(x+8)\)
\(3x(x-3)-2(5x+4)\)
\(3x(x-4)+2(x-4)\)
Solution
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(From Unit 2, Lesson 23.)