Lesson 13

Multiplying Complex Numbers

  • Let's multiply complex numbers.

Problem 1

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

A:

\(\text-6 + 10i\)

B:

\(6 + 10i\)

C:

\(\text-10 + 6i\)

D:

\(10+ 6i\)

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:”

\((7 + 2i) + (3 - 2i) = 10\)

\((2 + 2i)(2 + 2i) = 8i\)

  1. Check Noah’s arithmetic. Is it correct?
  2. 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 \(729^{\frac23}\)?

A:

243

B:

486

C:

\(9^2\)

D:

\(27^3\)

(From Unit 3, Lesson 4.)

Problem 5

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

  1. \(2x^2-\frac23= 5\frac13\)
  2. \((x+1)^2=81\)
  3. \(3x^2+14=12\)
(From Unit 3, Lesson 7.)

Problem 6

Plot each number in the complex plane.

  1. \(5i\)
  2. \(2+4i\)
  3. -3
  4. \(1 - 3i\)
  5. \(\text-5 - 2i\)
Coordinate plane. Horizontal axis, scale -6 to 6, by 2’s. Vertical axis, scale -6i to 6i, by 2i’s.
(From Unit 3, Lesson 11.)

Problem 7

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

A:

\(3x^2-12\)

B:

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

C:

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

D:

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

E:

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

F:

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

(From Unit 2, Lesson 23.)