11th grade Complex numbers in polar form worksheet

Complex numbers in polar form

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°?
2. 2.

   Milo plots z = -5 − 12i. To the nearest tenth of a degree, what is its argument θ, from 0° up to 360°?
3. 3.

   Noah plots z = 8 − 6i. To the nearest tenth of a degree, what is its argument θ, from 0° up to 360°?
4. 4.

   Pia plots z = -15 + 8i. To the nearest tenth of a degree, what is its argument θ, from 0° up to 360°?
5. 5.

   Tala changes z = -2 + 2√3i to polar form with θ from 0° up to 360°. Which is the polar form of z?

   • 4(cos 120° + i sin 120°)
   • 4(cos 60° + i sin 60°)
   • 4(cos 240° + i sin 240°)
   • 16(cos 120° + i sin 120°)
6. 6.

   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 150° + i sin 150°)
   • 6(cos 210° + i sin 210°)
7. 7.

   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 150° + i sin 150°)
   • 10(cos 300° + i sin 300°)
   • 10(cos 60° + i sin 60°)
   • 100(cos 300° + i sin 300°)
8. 8.

   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 135° + i sin 135°)
   • 98(cos 225° + i sin 225°)
   • 7√2(cos 45° + i sin 45°)
   • 7√2(cos 225° + i sin 225°)
9. 9.

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