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.

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)
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   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
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   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
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   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
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   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
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   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.

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