My Learning Cart
?
Categories
Account

Complex numbers

Download Q&A
Q. If z = re^(iθ), what is the value of z^3?
  • A. r^3 e^(i3θ)
  • B. r^3 e^(iθ)
  • C. 3re^(iθ)
  • D. r^3 e^(iθ^3)
Q. If z = re^(iθ), what is the value of |z|?
  • A. r
  • B. θ
  • C. re
  • D. 1
Q. If z = x + yi is a complex number such that |z| = 10, what is the equation of the circle in the complex plane?
  • A. x^2 + y^2 = 100
  • B. x^2 + y^2 = 10
  • C. x^2 + y^2 = 50
  • D. x^2 + y^2 = 25
Q. If z = x + yi, find the real part of z^3.
  • A. x^3 - 3xy^2
  • B. 3x^2y - y^3
  • C. x^3 + 3xy^2
  • D. 3x^2 - y^3
Q. If z1 = 1 + i and z2 = 1 - i, find z1 * z2.
  • A. 2
  • B. 0
  • C. 1
  • D. -1
Q. If z1 = 1 + i and z2 = 2 - 3i, find z1 * z2.
  • A. 7 - i
  • B. 7 + i
  • C. 5 - i
  • D. 5 + i
Q. If z1 = 1 + i and z2 = 2 - 3i, what is z1 * z2?
  • A. 5 - i
  • B. 8 - i
  • C. 7 + i
  • D. 1 + 5i
Q. If z1 = 1 + i and z2 = 2 - i, find z1 * z2.
  • A. 3 + i
  • B. 3 - i
  • C. 2 + 3i
  • D. 2 - 3i
Q. If z1 = 2 + 3i and z2 = 4 - 5i, then z1 + z2 is?
  • A. 6 - 2i
  • B. 6 + 2i
  • C. 2 - 2i
  • D. 2 + 2i
Q. If z1 = 2 + 3i and z2 = 4 - i, find z1 + z2.
  • A. 6 + 2i
  • B. 6 + 4i
  • C. 2 + 6i
  • D. 8 + 2i
Q. If z1 = 2 + 3i and z2 = 4 - i, what is z1 + z2?
  • A. 6 + 2i
  • B. 6 + 4i
  • C. 2 + 4i
  • D. 2 + 2i
Q. The argument of the complex number z = -1 - i is?
  • A. -3π/4
  • B. 3π/4
  • C. π/4
  • D. -π/4
Q. The product of two complex numbers z1 = 1 + i and z2 = 2 - i is?
  • A. 3 + i
  • B. 3 - i
  • C. 2 + 3i
  • D. 2 - 3i
Q. The real part of the complex number z = 4 - 3i is?
  • A. 4
  • B. -3
  • C. 3
  • D. 0
Q. The value of (1 + i)^2 is?
  • A. 2i
  • B. 2
  • C. 0
  • D. 1 + 2i
Q. What is the argument of the complex number z = -1 + 0i?
  • A. π
  • B. 0
  • C. π/2
  • D. -π
Q. What is the argument of the complex number z = -1 - i?
  • A. -3π/4
  • B. 3π/4
  • C. -π/4
  • D. π/4
Q. What is the conjugate of the complex number z = 2 + 5i?
  • A. 2 - 5i
  • B. 2 + 5i
  • C. -2 + 5i
  • D. -2 - 5i
Q. What is the conjugate of the complex number z = 5 - 2i?
  • A. 5 + 2i
  • B. 5 - 2i
  • C. 2 - 5i
  • D. 2 + 5i
Q. What is the conjugate of the complex number z = 5 - 6i?
  • A. 5 + 6i
  • B. 5 - 6i
  • C. 6 - 5i
  • D. 6 + 5i
Q. What is the modulus of the complex number z = -3 + 4i?
  • A. 5
  • B. 7
  • C. 3
  • D. 4
Q. What is the product of (1 + i) and (1 - i)?
  • A. 2
  • B. 0
  • C. 1
  • D. 1 + 0i
Q. What is the product of the complex numbers (1 + i) and (1 - i)?
  • A. 2
  • B. 0
  • C. 1
  • D. 1 + 0i
Q. What is the product of the complex numbers z1 = 1 + i and z2 = 1 - i?
  • A. 2
  • B. 0
  • C. 1
  • D. 1 + 0i
Q. What is the real part of the complex number 5 - 7i?
  • A. 5
  • B. -7
  • C. 0
  • D. 7
Q. What is the real part of the complex number z = 2e^(iπ/3)?
  • A. 1
  • B. 2
  • C. 3
  • D. 0
Q. What is the real part of the complex number z = 4e^(iπ/3)?
  • A. 2
  • B. 4
  • C. 2√3
  • D. 4√3
Q. What is the real part of the complex number z = 5 - 2i?
  • A. 5
  • B. -2
  • C. 2
  • D. 0
Q. What is the real part of the complex number z = 5 - 4i?
  • A. 5
  • B. -4
  • C. 4
  • D. 0
Q. What is the real part of the complex number z = 5 - 6i?
  • A. 5
  • B. -6
  • C. 11
  • D. 1
Showing 61 to 90 of 101 (4 Pages)

Complex Numbers MCQ & Objective Questions

Complex numbers play a crucial role in mathematics, especially in higher secondary education and competitive exams. Understanding complex numbers is essential for students aiming to excel in subjects like mathematics and physics. Practicing MCQs and objective questions on complex numbers not only enhances conceptual clarity but also boosts confidence, helping students score better in their exams.

What You Will Practise Here

  • Definition and properties of complex numbers
  • Representation of complex numbers in the Argand plane
  • Operations on complex numbers: addition, subtraction, multiplication, and division
  • Modulus and argument of complex numbers
  • Polar form and exponential form of complex numbers
  • De Moivre's theorem and its applications
  • Solving quadratic equations with complex roots

Exam Relevance

Complex numbers are a significant topic in various educational boards, including CBSE and State Boards, as well as competitive exams like NEET and JEE. Students can expect questions that test their understanding of definitions, properties, and applications of complex numbers. Common question patterns include solving equations, converting between forms, and applying De Moivre's theorem in problems.

Common Mistakes Students Make

  • Confusing the real and imaginary parts of complex numbers
  • Incorrectly applying the modulus and argument formulas
  • Struggling with conversions between rectangular and polar forms
  • Overlooking the significance of complex conjugates in calculations

FAQs

Question: What are complex numbers?
Answer: Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the imaginary part.

Question: How do I convert a complex number from rectangular to polar form?
Answer: To convert a complex number from rectangular form (a + bi) to polar form, calculate the modulus (r = √(a² + b²)) and the argument (θ = tan⁻¹(b/a)).

Now is the perfect time to enhance your understanding of complex numbers. Dive into our practice MCQs and test your knowledge to ensure you are well-prepared for your exams!

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks