Complex conjugates, and dividing complex numbers

Answer Key - Grade 11 Math Worksheet - Building Confidence

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

1. 1.

   Pia holds a mirror along the real axis to flip 4 − 7i. What is the conjugate of 4 − 7i?

   4 + 7i
2. 2.

   Tala writes the conjugate of -8 − 2i on a puzzle card. What is the conjugate of -8 − 2i?

   -8 + 2i
3. 3.

   Zee checks a reflection of 5 + i in the real axis. What is the conjugate of 5 + i?

   5 − i
4. 4.

   Esme multiplies 3 + 5i by its mirror image, 3 − 5i. What is (3 + 5i)(3 − 5i)?

   34
5. 5.

   Jun multiplies a number by its conjugate on a puzzle card. What is (7 − 2i)(7 + 2i)?

   53
6. 6.

   Kira works out (-1 + 6i)(-1 − 6i) on the board. What is (-1 + 6i)(-1 − 6i)?

   37
7. 7.

   Milo shares 12 − 8i into 4 equal steps from 0. What is (12 − 8i) ÷ 4?

   3 − 2i
8. 8.

   Noah divides a puzzle number by 5. What is (-15 + 10i) ÷ 5?

   -3 + 2i
9. 9.

   Pia's robot shrinks its trip from 0 to 6 + 9i down to one third. What is (6 + 9i) ÷ 3?

   2 + 3i
10. 10.

    Ren divides a grid map pin, 14 − 21i, by 7. What is (14 − 21i) ÷ 7?

    2 − 3i