Complex numbers in polar form

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   A drone's spot from home, in km, is z = 3 + 4i. Esme plots it on the complex plane. What is |z|, its distance from 0?

   5
2. 2.

   A boat's spot from the dock, in km, is z = -5 + 12i. Jun plots it on the complex plane. What is |z|, its distance from 0?

   13
3. 3.

   A robot's spot from its charger, in m, is z = 6 − 8i. Kira plots it on the complex plane. What is |z|, its distance from 0?

   10
4. 4.

   A kite's spot from the launch point, in m, is z = -8 − 15i. Luz plots it on the complex plane. What is |z|, its distance from 0?

   17
5. 5.

   Milo plots z = 4 + 4i at the point (4, 4) on the complex plane. What is its argument θ, from 0° up to 360°?

   45
6. 6.

   Noah plots z = -2i at the point (0, -2) on the complex plane. What is its argument θ, from 0° up to 360°?

   270
7. 7.

   Zee writes z = -5i in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of -5i?

   • 25(cos 270° + i sin 270°)
   • 5(cos 270° + i sin 270°)
   • 5(cos 90° + i sin 90°)
   • 5(cos 180° + i sin 180°)
8. 8.

   Esme writes z = 2 + 2i in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of 2 + 2i?

   • 8(cos 45° + i sin 45°)
   • 2√2(cos 45° + i sin 45°)
   • 4(cos 45° + i sin 45°)
   • 2√2(cos 315° + i sin 315°)
9. 9.

   Jun writes z = -4 in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of -4?

   • 4(cos 180° + i sin 180°)
   • 16(cos 180° + i sin 180°)
   • 4(cos 270° + i sin 270°)
10. 10.

    Kira writes z = -3 + 3i in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of -3 + 3i?

    • 3√2(cos 225° + i sin 225°)
    • 3√2(cos 135° + i sin 135°)
    • 3√2(cos 315° + i sin 315°)
    • 6(cos 135° + i sin 135°)