# Lesson 13

Multiplying Complex Numbers

- Let's multiply complex numbers.

### Problem 1

Which expression is equivalent to \(2i(5+3i)\)?

\(\text-6 + 10i\)

\(6 + 10i\)

\(\text-10 + 6i\)

\(10+ 6i\)

### 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.

### 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.

### Problem 4

Which expression is equal to \(729^{\frac23}\)?

243

486

\(9^2\)

\(27^3\)

### Problem 5

Find the solution(s) to each equation, or explain why there is no solution.

- \(2x^2-\frac23= 5\frac13\)
- \((x+1)^2=81\)
- \(3x^2+14=12\)

### Problem 6

Plot each number in the complex plane.

- \(5i\)
- \(2+4i\)
- -3
- \(1 - 3i\)
- \(\text-5 - 2i\)

### Problem 7

Select **all** the expressions that are equivalent to \((3x+2)(x-4)\) for all real values of \(x\).

\(3x^2-12\)

\(3x^2-10x-8\)

\(3(x^2 + 2x - 4)\)

\(3(x^2-3x)-(x+8)\)

\(3x(x-3)-2(5x+4)\)

\(3x(x-4)+2(x-4)\)