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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

What is the modulus of 3+4i3+4i?

Please select an answer first.

Correct answer: A

The correct answer is 5.

  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 modulus is sqrt(3^2+4^2) = sqrt(25) = 5.
  3. Check the result: The correct answer is 5.

The modulus is sqrt(3^2+4^2) = sqrt(25) = 5.

2. QuestionMultiple choice

What is the distance from the origin to −6+8i-6+8i in the complex plane?

Please select an answer first.

Correct answer: B

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: The distance is the modulus: sqrt((-6)^2+8^2) = sqrt(100) = 10.
  3. Check the result: The correct answer is 10.

The distance is the modulus: sqrt((-6)^2+8^2) = sqrt(100) = 10.

3. QuestionMultiple choice

What is the conjugate of −2+5i-2+5i?

Please select an answer first.

Correct answer: C

The correct answer is −2−5i-2-5i.

  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: Keep the real part and change the sign of the imaginary part.
  3. Check the result: The correct answer is −2−5i-2-5i.

Keep the real part and change the sign of the imaginary part.

4. QuestionMultiple choice

Which ordered pair represents 1−3i1-3i?

Please select an answer first.

Correct answer: D

The correct answer is (1,−3)(1,-3).

  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 complex number a+bi corresponds to the point (a,b), so 1-3i maps to (1,-3).
  3. Check the result: The correct answer is (1,−3)(1,-3).

The complex number a+bi corresponds to the point (a,b), so 1-3i maps to (1,-3).

5. QuestionMultiple choice

What is the modulus of 6−8i6-8i?

Please select an answer first.

Correct answer: A

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: Compute sqrt(6^2+(-8)^2) = sqrt(100) = 10.
  3. Check the result: The correct answer is 10.

Compute sqrt(6^2+(-8)^2) = sqrt(100) = 10.

6. QuestionMultiple choice

In which quadrant is −2+3i-2+3i located?

Please select an answer first.

Correct answer: B

The correct answer is Quadrant II.

  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 real part is negative and the imaginary part is positive, placing the point in Quadrant II.
  3. Check the result: The correct answer is Quadrant II.

The real part is negative and the imaginary part is positive, placing the point in Quadrant II.

7. QuestionMultiple choice

What is the real part of 4−7i4-7i?

Please select an answer first.

Correct answer: C

The correct answer is 4.

  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 real part is the coefficient without i, which is 4.
  3. Check the result: The correct answer is 4.

The real part is the coefficient without i, which is 4.

8. QuestionMultiple choice

What is ∣3+4i∣|3+4i|?

Please select an answer first.

Correct answer: D

The correct answer is 5.

  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: Use the modulus formula: |3+4i| = sqrt(3^2+4^2) = 5.
  3. Check the result: The correct answer is 5.

Use the modulus formula: |3+4i| = sqrt(3^2+4^2) = 5.

9. QuestionMultiple choice

What is the midpoint of the points represented by 2+i2+i and 6+5i6+5i?

Please select an answer first.

Correct answer: A

The correct answer is 4+3i4+3i.

  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: Average the real parts and imaginary parts: ((2+6)/2) + ((1+5)/2)i = 4+3i.
  3. Check the result: The correct answer is 4+3i4+3i.

Average the real parts and imaginary parts: ((2+6)/2) + ((1+5)/2)i = 4+3i.

10. QuestionMultiple choice

What is the reflection of −1+2i-1+2i across the real axis?

Please select an answer first.

Correct answer: B

The correct answer is −1−2i-1-2i.

  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: Reflection across the real axis changes the sign of the imaginary part, producing the conjugate.
  3. Check the result: The correct answer is −1−2i-1-2i.

Reflection across the real axis changes the sign of the imaginary part, producing the conjugate.

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