Quadratic equations with complex solutions

Answer Key - Grade 11 Math Worksheet

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

1. 1.

   Ren solves x² − 4x + 13 = 0 with the quadratic formula. What is the solution with the + sign, in a + bi form?

   2 + 3i
2. 2.

   Zee's robot solves x² + 2x + 17 = 0. What is the solution with the + sign, in a + bi form?

   -1 + 4i
3. 3.

   Esme solves x² − 10x + 26 = 0 for a math club puzzle. What is the solution with the + sign, in a + bi form?

   5 + i
4. 4.

   Jun solves 2x² − 4x + 10 = 0 with the quadratic formula. What is the solution with the + sign, in a + bi form?

   1 + 2i
5. 5.

   Kira solves 4x² + 8x + 5 = 0. Use fractions if needed. What is the solution with the + sign, in a + bi form?

   -1 + (1/2)i
6. 6.

   Luz's robot solves 9x² − 6x + 5 = 0. Use fractions. What is the solution with the + sign, in a + bi form?

   1/3 + (2/3)i
7. 7.

   Milo solves 2x² + 2x + 1 = 0. Use fractions. What is the solution with the + sign, in a + bi form?

   -1/2 + (1/2)i
8. 8.

   Noah solves (x − 3)² = -25 by taking square roots. What is the solution whose i part is positive, in a + bi form?

   3 + 5i
9. 9.

   Pia solves (x + 2)² = -9 by taking square roots. What is the solution whose i part is positive, in a + bi form?

   -2 + 3i
10. 10.

    Ren solves (x − 5)² = -49 by taking square roots. What is the solution whose i part is positive, in a + bi form?

    5 + 7i