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.

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.

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