Complex numbers in polar form

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Luz plots z = -3 + 4i. To the nearest tenth of a degree, what is its argument θ, from 0° up to 360°?

   126.9
2. 2.

   Noah plots z = 8 − 6i. To the nearest tenth of a degree, what is its argument θ, from 0° up to 360°?

   323.1
3. 3.

   Pia plots z = -15 + 8i. To the nearest tenth of a degree, what is its argument θ, from 0° up to 360°?

   151.9
4. 4.

   Zee changes z = -3√3 − 3i to polar form with θ from 0° up to 360°. Which is the polar form of z?

   • 6(cos 240° + i sin 240°)
   • 6(cos 30° + i sin 30°)
   • 6(cos 210° + i sin 210°)
   • 6(cos 150° + i sin 150°)
5. 5.

   Esme changes z = 5 − 5√3i to polar form with θ from 0° up to 360°. Which is the polar form of z?

   • 10(cos 300° + i sin 300°)
   • 100(cos 300° + i sin 300°)
   • 10(cos 150° + i sin 150°)
   • 10(cos 60° + i sin 60°)
6. 6.

   Jun changes z = -7 − 7i to polar form with θ from 0° up to 360°. Which is the polar form of z?

   • 7√2(cos 225° + i sin 225°)
   • 7√2(cos 135° + i sin 135°)
   • 7√2(cos 45° + i sin 45°)
   • 98(cos 225° + i sin 225°)
7. 7.

   Kira changes z = 6(cos 30° + i sin 30°) to the form a + bi. Which is z in the form a + bi?

   • 3 + 3√3i
   • √3/2 + (1/2)i
   • 3√3 + 3i
8. 8.

   Luz changes z = 8(cos 150° + i sin 150°) to the form a + bi. Which is z in the form a + bi?

   • 4√3 + 4i
   • -4√3 + 4i
   • -√3/2 + (1/2)i
   • 4 − 4√3i
9. 9.

   Milo changes z = 10(cos 240° + i sin 240°) to the form a + bi. Which is z in the form a + bi?

   • -5 − 5√3i
   • 5 + 5√3i
   • -5√3 − 5i
   • -1/2 − (√3/2)i
10. 10.

    Noah changes z = 4(cos 315° + i sin 315°) to the form a + bi. Which is z in the form a + bi?

    • 2√2 − 2√2i
    • -2√2 + 2√2i
    • 2√2 + 2√2i
    • √2/2 − (√2/2)i