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.

   Ren flips the pin at -3 + 5i across the real axis on a grid map. What is the conjugate of -3 + 5i?

   -3 − 5i
3. 3.

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

   -8 + 2i
4. 4.

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

   5 − i
5. 5.

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

   34
6. 6.

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

   53
7. 7.

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

   37
8. 8.

   Luz multiplies two mirror pins on a grid map. What is (4 + 5i)(4 − 5i)?

   41
9. 9.

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

   3 − 2i
10. 10.

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

    -3 + 2i