Complex numbers in polar form

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Pia changes z = 1 − √3i to polar form with θ in radians, from 0 up to 2π. Which is the polar form of z?

   • 2(cos 5π/3 + i sin 5π/3)
   • 2(cos 5π/6 + i sin 5π/6)
   • 2(cos π/3 + i sin π/3)
   • 4(cos 5π/3 + i sin 5π/3)
2. 2.

   Zee changes z = -4 − 4i to polar form with θ in radians, from 0 up to 2π. Which is the polar form of z?

   • 4√2(cos π/4 + i sin π/4)
   • 4√2(cos 5π/4 + i sin 5π/4)
   • 32(cos 5π/4 + i sin 5π/4)
   • 4√2(cos 3π/4 + i sin 3π/4)
3. 3.

   Esme changes z = 3√3 + 3i to polar form with θ in radians, from 0 up to 2π. Which is the polar form of z?

   • 6(cos π/3 + i sin π/3)
   • 6(cos π/6 + i sin π/6)
   • 36(cos π/6 + i sin π/6)
   • 6(cos 11π/6 + i sin 11π/6)
4. 4.

   Jun changes z = 6(cos 5π/6 + i sin 5π/6) to the form a + bi. Which is z in the form a + bi?

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

   Kira changes z = 4(cos 4π/3 + i sin 4π/3) to the form a + bi. Which is z in the form a + bi?

   • -1/2 − (√3/2)i
   • 2 + 2√3i
   • -2√3 − 2i
   • -2 − 2√3i
6. 6.

   Luz changes z = 8(cos 7π/4 + i sin 7π/4) to the form a + bi. Which is z in the form a + bi?

   • 4√2 + 4√2i
   • √2/2 − (√2/2)i
   • -4√2 + 4√2i
   • 4√2 − 4√2i
7. 7.

   Milo changes z = 10(cos π/3 + i sin π/3) to the form a + bi. Which is z in the form a + bi?

   • 5√3 + 5i
   • 5 + 5√3i
   • 1/2 + (√3/2)i
8. 8.

   A drone flies from home to z = 12(cos 150° + i sin 150°) km; east is real and north is imaginary. Noah tracks it. What is b, the north part of z?

   6
9. 9.

   A boat sails from the dock to z = 14(cos 210° + i sin 210°) km; east is real and north is imaginary. Pia tracks it. What is b, the north part of z?

   -7
10. 10.

    A kite drifts from the launch point to z = 16(cos 30° + i sin 30°) m; east is real and north is imaginary. Zee tracks it. What is b, the north part of z?

    8