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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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5 Tests
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1. Test

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

Simplify x3⋅x4x^3\cdot x^4.

Please select an answer first.

Correct answer: A

The correct answer is x7x^7.

  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: When multiplying powers with the same base, add the exponents: x^3 · x^4 = x^(3+4) = x^7.
  3. Check the result: The correct answer is x7x^7.

When multiplying powers with the same base, add the exponents: x^3 · x^4 = x^(3+4) = x^7.

2. QuestionMultiple choice

Simplify a5a2\frac{a^5}{a^2} for a≠0a\ne0.

Please select an answer first.

Correct answer: B

The correct answer is a3a^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: When dividing powers with the same nonzero base, subtract the exponents: a^(5-2) = a^3.
  3. Check the result: The correct answer is a3a^3.

When dividing powers with the same nonzero base, subtract the exponents: a^(5-2) = a^3.

3. QuestionMultiple choice

Simplify (2x3)2(2x^3)^2.

Please select an answer first.

Correct answer: C

The correct answer is 4x64x^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: Square the coefficient and multiply the exponent by 2: 2^2(x^3)^2 = 4x^6.
  3. Check the result: The correct answer is 4x64x^6.

Square the coefficient and multiply the exponent by 2: 2^2(x^3)^2 = 4x^6.

4. QuestionMultiple choice

Evaluate i2i^2.

Please select an answer first.

Correct answer: D

The correct answer is -1.

  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 imaginary unit is defined by i^2 = -1.
  3. Check the result: The correct answer is -1.

The imaginary unit is defined by i^2 = -1.

5. QuestionMultiple choice

What is the real part of 3−7i3-7i?

Please select an answer first.

Correct answer: A

The correct answer is 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: In a + bi, the real part is a, so the real part of 3 - 7i is 3.
  3. Check the result: The correct answer is 3.

In a + bi, the real part is a, so the real part of 3 - 7i is 3.

6. QuestionMultiple choice

What is the imaginary part of −2+5i-2+5i?

Please select an answer first.

Correct answer: B

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: In a + bi, the imaginary part is the coefficient b of i, so it is 5.
  3. Check the result: The correct answer is 5.

In a + bi, the imaginary part is the coefficient b of i, so it is 5.

7. QuestionMultiple choice

Simplify (4+3i)+(2−i)(4+3i)+(2-i).

Please select an answer first.

Correct answer: C

The correct answer is 6+2i6+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: Add real parts and imaginary parts separately: (4+2) + (3-1)i = 6 + 2i.
  3. Check the result: The correct answer is 6+2i6+2i.

Add real parts and imaginary parts separately: (4+2) + (3-1)i = 6 + 2i.

8. QuestionMultiple choice

Simplify (5−2i)−(1+4i)(5-2i)-(1+4i).

Please select an answer first.

Correct answer: D

The correct answer is 4−6i4-6i.

  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: Subtract corresponding parts: (5-1) + (-2-4)i = 4 - 6i.
  3. Check the result: The correct answer is 4−6i4-6i.

Subtract corresponding parts: (5-1) + (-2-4)i = 4 - 6i.

9. QuestionMultiple choice

What is the additive inverse of 4−3i4-3i?

Please select an answer first.

Correct answer: A

The correct answer is −4+3i-4+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: The additive inverse changes the signs of both the real and imaginary parts.
  3. Check the result: The correct answer is −4+3i-4+3i.

The additive inverse changes the signs of both the real and imaginary parts.

10. QuestionMultiple choice

Evaluate i6i^6.

Please select an answer first.

Correct answer: B

The correct answer is -1.

  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 powers cycle every four: i^6 = i^4 · i^2 = 1 · (-1) = -1.
  3. Check the result: The correct answer is -1.

The powers cycle every four: i^6 = i^4 · i^2 = 1 · (-1) = -1.

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