Algebra of Complex Numbers Quiz - CBSE Class 11 Mathematics

Free practice quiz: Algebra of Complex Numbers (CBSE Class 11 Mathematics). 19 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 11 Mathematics practice quiz has 19 multiple-choice questions on Algebra of Complex Numbers, and 19 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.

Sample questions

1. What is the sum of (3 + 4i) and (5 + 6i)?

   1. 8 + 10i
   2. -2 + 2i
   3. 15 + 24i
   4. 2 - 2i
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   Answer: A. 8 + 10i

   To find the sum, add the real parts and the imaginary parts separately: (3 + 5) + (4i + 6i) = 8 + 10i.

2. If z = -2 + i, what is |z|, the modulus of z?

   1. √5
   2. √2
   3. 5
   4. 3
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   Answer: A. √5

   The modulus of a complex number z = a + bi is |z| = √(a² + b²). Thus, |-2 + i| = √((-2)² + 1²) = √(4 + 1) = √5.

3. Simplify (1 + i)^2.

   1. 0
   2. i
   3. 2i
   4. 2i + 1
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   Answer: C. 2i

   Use the identity (a + b)^2 = a^2 + 2ab + b^2. Here, (1 + i)^2 = 1 + 2*i + i^2 = 1 + 2i - 1 = 2i.

4. Find the solution of i^15.

   1. -i
   2. -1
   3. 1
   4. i
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   Answer: A. -i

   i repeats every four powers: i, -1, -i, and 1. Dividing 15 by 4 gives a remainder of 3, so i^15 = i^3 = -i.

5. What is the principal argument of -1 - i?

   1. -3π/4
   2. π/4
   3. 3π/4
   4. 4π/3
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   Answer: A. -3π/4

   The principal argument, θ, of a complex number -1 - i is the angle the line makes with the positive direction of the x-axis. It is in the third quadrant, so θ = -3π/4.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the product of (2 + 3i) and (1 - i)?
2. What is the conjugate of the complex number 4 + 7i?
3. Which number is represented by i^4?
4. What is the result of (3 + 4i) - (1 - 2i)?
5. If z1 = 1 + i and z2 = 0.5 - 0.5i, what is z1 * z2?
6. Which of the following represents the imaginary part of the complex number 3/2 + 5i?
7. For z = 2 + 3i, what is |z|^2?
8. If w = 4i and z = 1 - i, find w/z.
9. What is the result of √-1 * √-1?
10. If z = 6 + 8i, express z in its polar form.
11. If z = 1 + i, which operation will convert z into Polar Form r*(cos θ + i*sin θ)?
12. If z^2 = -16, what are the possible values of z?
13. Using De Moivre's Theorem, find (1 + i)³.
14. Solve z^4 = 1 + 0i and determine the roots in complex numbers.

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