The imaginary unit i, and its powers

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Kira's robot makes 30 quarter turns about 0, starting at 1. Each turn is one factor of i. What is i³⁰?

   -1
2. 2.

   Luz programs the robot for 51 quarter turns about 0, starting at 1. What is i⁵¹?

   -i
3. 3.

   Milo needs i⁴⁵ for a math club puzzle. Each factor of i is a quarter turn about 0, starting at 1. What is i⁴⁵?

   i
4. 4.

   Noah follows 72 quarter turns about 0 on a grid map, starting at 1. What is i⁷²?

   1
5. 5.

   Pia simplifies √(-50) for a math club card. Which is √(-50) in simplest form?

   • -5√2
   • -5i√2
   • 5i√2
   • 5√2
6. 6.

   Tala checks a puzzle answer for √(-45). Which is √(-45) in simplest form?

   • 3i√5
   • -3√5
   • -3i√5
   • 3√5
7. 7.

   Zee simplifies √(-72). Which is √(-72) in simplest form?

   • -6√2
   • -6i√2
   • 6i√2
   • 6√2
8. 8.

   Esme squares 5i on the complex plane. The point moves farther out and turns. What is (5i)²?

   -25
9. 9.

   Jun's robot starts at 2i and is cubed, so its distance from 0 grows and it turns. What is (2i)³?

   -8i
10. 10.

    Kira writes (3i)³ on a puzzle card. What is (3i)³?

    -27i