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Complex Numbers Practice Tests

These Grade 11 Math practice tests develop fluency with the imaginary unit, complex-number operations, conjugates, modulus, the complex plane, quadratic equations with nonreal roots, and polynomial root relationships.

Skills covered

  • Using powers of the imaginary unit and identifying real and imaginary parts
  • Adding, subtracting, multiplying, dividing, and simplifying complex numbers
  • Using conjugates, modulus, distance, midpoint, and complex-plane coordinates
  • Solving quadratic equations with negative discriminants
  • Applying conjugate roots, Vieta’s formulas, factorization, and the Fundamental Theorem of Algebra

How to use these practice tests

Replace i² with -1, group real and imaginary terms, use a conjugate when rationalizing a denominator, and verify roots by substitution or factoring.

For more Grade 11 Math practice, return to the Grade 11 Math category.

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Grade 11 Complex Numbers Practice Tests

Practice Grade 11 Math questions about the imaginary unit, complex-number operations, conjugates, modulus, the complex plane, quadratic equations, and polynomial roots.

Choose the best answer. Use i^2 = -1, combine real and imaginary parts separately, and check restrictions and roots carefully.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

Solve x2+9=0x^2+9=0.

Please select an answer first.

Correct answer: A

The correct answer is x=±3ix=\pm3i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: x^2 = -9, so x = ±sqrt(-9) = ±3i.
  3. Check the result: The correct answer is x=±3ix=\pm3i.

x^2 = -9, so x = ±sqrt(-9) = ±3i.

2. QuestionMultiple choice

Solve x2+4x+13=0x^2+4x+13=0.

Please select an answer first.

Correct answer: B

The correct answer is x=−2±3ix=-2\pm3i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: The quadratic formula gives (-4 ± sqrt(-36))/2 = -2 ± 3i.
  3. Check the result: The correct answer is x=−2±3ix=-2\pm3i.

The quadratic formula gives (-4 ± sqrt(-36))/2 = -2 ± 3i.

3. QuestionMultiple choice

Solve x2−6x+25=0x^2-6x+25=0.

Please select an answer first.

Correct answer: C

The correct answer is x=3±4ix=3\pm4i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: The quadratic formula gives (6 ± sqrt(-64))/2 = 3 ± 4i.
  3. Check the result: The correct answer is x=3±4ix=3\pm4i.

The quadratic formula gives (6 ± sqrt(-64))/2 = 3 ± 4i.

4. QuestionMultiple choice

Solve x2+2x+5=0x^2+2x+5=0.

Please select an answer first.

Correct answer: D

The correct answer is x=−1±2ix=-1\pm2i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: The quadratic formula gives (-2 ± sqrt(-16))/2 = -1 ± 2i.
  3. Check the result: The correct answer is x=−1±2ix=-1\pm2i.

The quadratic formula gives (-2 ± sqrt(-16))/2 = -1 ± 2i.

5. QuestionMultiple choice

Solve x2+1=0x^2+1=0.

Please select an answer first.

Correct answer: A

The correct answer is x=±ix=\pm i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: x^2 = -1, and the two complex solutions are x = i and x = -i.
  3. Check the result: The correct answer is x=±ix=\pm i.

x^2 = -1, and the two complex solutions are x = i and x = -i.

6. QuestionMultiple choice

Solve x2−4x+8=0x^2-4x+8=0.

Please select an answer first.

Correct answer: B

The correct answer is x=2±2ix=2\pm2i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: The quadratic formula gives (4 ± sqrt(-16))/2 = 2 ± 2i.
  3. Check the result: The correct answer is x=2±2ix=2\pm2i.

The quadratic formula gives (4 ± sqrt(-16))/2 = 2 ± 2i.

7. QuestionMultiple choice

What is the sum of the roots of x2+6x+13=0x^2+6x+13=0?

Please select an answer first.

Correct answer: C

The correct answer is -6.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: By Vieta's formula, the sum of the roots is -b/a = -6/1 = -6.
  3. Check the result: The correct answer is -6.

By Vieta's formula, the sum of the roots is -b/a = -6/1 = -6.

8. QuestionMultiple choice

What is the product of the roots of x2+2x+10=0x^2+2x+10=0?

Please select an answer first.

Correct answer: D

The correct answer is 10.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: By Vieta's formula, the product of the roots is c/a = 10/1 = 10.
  3. Check the result: The correct answer is 10.

By Vieta's formula, the product of the roots is c/a = 10/1 = 10.

9. QuestionMultiple choice

What is the discriminant of x2+4x+8=0x^2+4x+8=0?

Please select an answer first.

Correct answer: A

The correct answer is -16.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: The discriminant is b^2-4ac = 4^2 - 4(1)(8) = 16 - 32 = -16.
  3. Check the result: The correct answer is -16.

The discriminant is b^2-4ac = 4^2 - 4(1)(8) = 16 - 32 = -16.

10. QuestionMultiple choice

Solve x2−2x+5=0x^2-2x+5=0.

Please select an answer first.

Correct answer: B

The correct answer is x=1±2ix=1\pm2i.

  1. Identify the complex-number structure: Determine the real part, imaginary part, powers of i, conjugate, modulus, operation, or equation involved.
  2. Apply the complex-number relationship: The quadratic formula gives (2 ± sqrt(-16))/2 = 1 ± 2i.
  3. Check the result: The correct answer is x=1±2ix=1\pm2i.

The quadratic formula gives (2 ± sqrt(-16))/2 = 1 ± 2i.

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