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Cogito

Integrated Math 2 · Chapter 3 · Lesson 2

Practice Worksheet

Arithmetic With Complex Numbers

Treat i like a variable, then simplify.

12 problems · about 21 minutes · N-CN.A.2

NameDate

Figure — use these to answer the problems

Adding complex numbers adds the components, exactly like adding vectors on this plane.
  • Vector a(3, 2)
  • Vector b(1, 3)
  • a + b(4, 5)
Real part of the first3
Imaginary part of the first2
Real part of the second1
Imaginary part of the second3
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. (4 + 3i)(4 − 3i). What is the result?

    Answer

  2. Why does multiplying by the conjugate give a real number?

    • The imaginary terms cancel and i² turns the sign.
    • It is a definition of the conjugate.

  3. (2 + 3i) + (4 + i). Real part?

    Answer

  4. Same sum. Imaginary coefficient?

    Answer

  5. (5 + 2i) − (3 + 6i). Real part?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Same difference. Imaginary coefficient?

    Answer

  2. (1 + i)(1 − i). What is the result?

    Answer

  3. (2 + 5i)(2 − 5i). What is the result?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Put the division process in order.

    Write 1 to 4 in the boxes to put these in order.

    • Write the conjugate of the denominator.
    • Multiply top and bottom by it.
    • Replace every i squared with negative one.
    • Write the answer as a + bi.

  2. (3 + i)(3 − i). What is the result?

    Answer

  3. The Sum

    (3 + 2i) + (1 + 5i). What is the imaginary coefficient?

    Answer

  4. The Conjugate

    (3 + 4i)(3 − 4i). What is the result?

    Answer