Complex conjugates, and dividing complex numbers

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Jun works out (4 − i) ÷ (2 + 3i). Write the answer in a + bi form, with fractions. What is (4 − i) ÷ (2 + 3i)?

   5/13 − (14/13)i
2. 2.

   Kira's robot divides 1 + 4i by 3 − i. What is (1 + 4i) ÷ (3 − i) in a + bi form?

   -1/10 + (13/10)i
3. 3.

   Luz divides two grid map pins. Write the answer in a + bi form, with fractions. What is (-2 + i) ÷ (3 + 4i)?

   -2/25 + (11/25)i
4. 4.

   Milo has a puzzle: (1 + i) times a number is 4 + 2i. What is the number, in a + bi form?

   3 − i
5. 5.

   Noah's robot multiplied a number by 2 − i and got 5. What was the number, in a + bi form?

   2 + i
6. 6.

   Pia writes a riddle: (3 + i) times a number is 10i. What is the number, in a + bi form?

   1 + 3i
7. 7.

   Tala finds the number that multiplies 3 + 4i to make 1. What is 1 ÷ (3 + 4i) in a + bi form?

   3/25 − (4/25)i
8. 8.

   Zee writes 1 ÷ (1 − 2i) on the board. Write it in a + bi form, with fractions. What is 1 ÷ (1 − 2i)?

   1/5 + (2/5)i
9. 9.

   Esme's robot needs the reciprocal of 2 + i. What is 1 ÷ (2 + i) in a + bi form?

   2/5 − (1/5)i
10. 10.

    Jun finds the reciprocal of a grid map pin, -1 + 3i. What is 1 ÷ (-1 + 3i) in a + bi form?

    -1/10 − (3/10)i