Complex conjugates, and dividing complex numbers

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Tala divides on a math club card. Write the answer in a + bi form. What is (5 + 5i) ÷ (1 + 2i)?

   3 − i
2. 2.

   Zee divides 3 − i by 1 − i on the board. Write the answer in a + bi form. What is (3 − i) ÷ (1 − i)?

   2 + i
3. 3.

   Esme's robot undoes a multiply by 2 + i. What is (-4 + 3i) ÷ (2 + i) in a + bi form?

   -1 + 2i
4. 4.

   Kira divides a puzzle number by 2i. Write the answer in a + bi form. What is (6 + 4i) ÷ (2i)?

   2 − 3i
5. 5.

   Luz works out (8 − 12i) ÷ (4i) on the board. What is (8 − 12i) ÷ (4i) in a + bi form?

   -3 − 2i
6. 6.

   Milo's robot divides its spot by 5i, a quarter turn back and a shrink. What is (-5 + 10i) ÷ (5i)?

   2 + i
7. 7.

   Pia wants to divide (7 − i) by (2 − 3i). What should the top and bottom both be multiplied by?

   • 2 + 3i
   • 7 + i
   • -2 − 3i
   • 2 − 3i
8. 8.

   Ren divides (4 + 5i) by (-1 + 2i) on the board. What should the top and bottom both be multiplied by?

   • -1 − 2i
   • -1 + 2i
   • 4 − 5i
   • 1 + 2i
9. 9.

   Tala uses a mirror idea to divide (-3 + 2i) by (5 + 4i). What should the top and bottom both be multiplied by?

   • -5 + 4i
   • 5 − 4i
   • -3 − 2i
   • 5 + 4i
10. 10.

    Zee divides two grid map pins: (6 − 5i) by (-3 − i). What should the top and bottom both be multiplied by?

    • 6 + 5i
    • -3 + i
    • -3 − i
    • 3 − i