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Cogito

Precalculus · Chapter 5 · Lesson 3

Practice Worksheet

Complex Numbers in Polar Form

Multiplying becomes rotating.

12 problems · about 22 minutes · TEKS P.4.F

NameDate

Figure — use these to answer the problems

Treat each arrow as a complex number. The modulus is its length and the argument is its angle.
  • Vector a(3, 4) · length 5
  • Vector b(1, 1) · length 1.41
Real part of a3
Imaginary part of a4
Real part of b1
Imaginary part of b1
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. What is the modulus of 8 + 6i?

    Answer

  2. What happens to the arguments when two complex numbers are multiplied?

    • They add.
    • They multiply.

  3. Modulus of 3 + 4i?

    Answer

  4. Modulus of 5i?

    Answer

  5. Argument of 4i, in degrees?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. Moduli 3 and 4 multiplied. What is the modulus of the product?

    Answer

  2. Arguments 40° and 25°, multiplied. What is the argument of the product, in degrees?

    Answer

  3. Modulus 2, argument 20°, raised to the 4th power. What is the new argument, in degrees?

    Answer

Stretch Yourself

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

4 problems

  1. Sort each operation by what happens to the modulus and the argument.

    Write each item under the heading it belongs to: r₁ × r₂ when multiplying · rⁿ when taking a power · θ₁ + θ₂ when multiplying · nθ when taking a power

    Moduli multiply

    Arguments add

  2. Modulus 3, argument 10°, cubed. What is the new modulus?

    Answer

  3. The Modulus

    What is the modulus of 6 + 8i?

    Answer

  4. The Power

    A complex number has modulus 2 and argument 30°. What is the modulus of its cube?

    Answer