The imaginary unit i, and its powers

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Esme sorts puzzle cards for math club. One card says √(-49). What is √(-49) written with i?

   7i
2. 2.

   Jun copies √(-81) onto the board. What is √(-81) written with i?

   9i
3. 3.

   Kira finds √(-121) on a math club card. What is √(-121) written with i?

   11i
4. 4.

   Luz marks √(-64) on a grid map of the complex plane. What is √(-64) written with i?

   8i
5. 5.

   Milo's robot starts at 1 on the complex plane. Each factor of i turns it a quarter turn about 0. What is i³?

   -i
6. 6.

   Pia draws quarter turns about 0, starting at 1, one turn for each factor of i. What is i⁵?

   i
7. 7.

   Ren traces quarter turns about 0 on the complex plane, starting at 1, one for each factor of i. What is i⁷?

   -i
8. 8.

   Tala rewrites a puzzle card, 3 + √(-16), as one point on the complex plane. What is 3 + √(-16) in a + bi form?

   3 + 4i
9. 9.

   Zee plots -5 + √(-36) on a grid map. What is -5 + √(-36) in a + bi form?

   -5 + 6i
10. 10.

    Esme simplifies 2 − √(-25) for the class board. What is 2 − √(-25) in a + bi form?

    2 − 5i