Polar Form of Complex Numbers Quiz - CBSE Class 11 Mathematics

Free practice quiz: Polar Form of Complex Numbers (CBSE Class 11 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.

This CBSE Class 11 Mathematics practice quiz has 18 multiple-choice questions on Polar Form of Complex Numbers, and 18 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. Convert the complex number z = 1 + i to polar form.

   1. √2(cos π/4 + i sin π/4)
   2. √2(cos 3π/4 + i sin 3π/4)
   3. √2(cos π/3 + i sin π/3)
   4. √2(cos π/6 + i sin π/6)
   Show answer

   Answer: A. √2(cos π/4 + i sin π/4)

   The complex number z = 1 + i has a modulus r = √(1^2 + 1^2) = √2 and argument θ = tan⁻¹(1/1) = π/4. Thus, in polar form, z = √2(cos π/4 + i sin π/4).

2. Given the complex number z = -2(cos π/4 + i sin π/4), find its modulus.

   1. 2
   2. 2√2
   3. √2
   4. 1
   Show answer

   Answer: A. 2

   The modulus of z = r(cos θ + i sin θ) is given directly by r. Here, the modulus is |z| = r = 2.

3. Find the rectangular form for the polar complex number z = 4cis3π/2.

   1. -4i
   2. 4
   3. 4i
   4. 0
   Show answer

   Answer: A. -4i

   z = 4(cos 3π/2 + i sin 3π/2) = 4(0 - i) = -4i.

4. What is the argument θ of z = -4 + 4i in its polar form?

   1. 3π/4
   2. π/4
   3. 5π/4
   4. 7π/4
   Show answer

   Answer: A. 3π/4

   z = -4 + 4i is in the second quadrant, arg θ = tan⁻¹(-1) + π = 3π/4.

5. Evaluate (2cis3π/8)² using De Moivre's Theorem.

   1. 4cis3π/4
   2. 4cis5π/4
   3. 8cis3π/4
   4. 8cis3π/8
   Show answer

   Answer: A. 4cis3π/4

   Using De Moivre's Theorem, (r cis θ)^n = r^n cis(nθ). For n = 2, r = 2, and θ = 3π/8, (2cis3π/8)² = 4cis(6π/8) = 4cis3π/4.

More questions in this quiz

Answers and explanations are in the full quiz.

1. What is the modulus of the complex number z = 3 + 4i in polar form?
2. Convert the polar form of z = 2(cos π/3 + i sin π/3) to its rectangular form.
3. The complex number z = 8i can be written in polar form as r(cos θ + i sin θ). Determine θ.
4. Calculate the polar form of the complex number z = -1 - i.
5. Express z = 5cisπ/6 as a rectangular form.
6. Calculate the product of two complex numbers in polar form: z₁ = 3cisπ/4 and z₂ = 2cisπ/6.
7. If z = 6(cos 2π/3 + i sin 2π/3), what is the rectangular form?
8. If z = 2(cos π/8 + i sin π/8), find z^2.
9. Express z = √3 - i in polar form.
10. Determine the argument for the complex number z = 1 - i√3.
11. If z = -2(cos π/3 + i sin π/3), determine its reciprocal in polar form.
12. For z = 4cis(-π/4), find the eighth power using De Moivre's Theorem.
13. Compute (1 + i√3)^6 using its polar form.

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