💬 Discord
Login

Complex Numbers Practice Questions

JEE · Mathematics · 1613 free MCQs with instant results and detailed explanations.

1613
Total
375
Easy
712
Medium
526
Hard

Start Practicing Complex Numbers

Take a timed quiz or customize your practice session

Quick Quiz (10 Qs) → Mock Test (25 Qs) ⚙ Customize

Topics in Complex Numbers

Algebra of Complex Numbers 248
Cube Roots of Unity 278
Modulus and Argument 248
De Moivre's Theorem 276
Argand Plane 272
Polar Form 291

Sample Questions from Complex Numbers

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the sum of the complex numbers 3 + 4i and 1 - 2i?
A. 4 + 2i
B. 3 + 2i
C. 2 + 6i
D. 5 + 6i
Show Answer & Explanation
Correct Answer: A
To find the sum of two complex numbers, we add their real parts and imaginary parts separately. Here, (3 + 1) + (4 - 2)i = 4 + 2i.
Q2
Easy
If z = 5 + 3i, what is the conjugate of z?
A. 5 - 3i
B. -5 + 3i
C. -5 - 3i
D. 5 + 3i
Show Answer & Explanation
Correct Answer: A
The conjugate of a complex number a + bi is defined as a - bi. Thus, the conjugate of 5 + 3i is 5 - 3i.
Q3
Easy
Which of the following represents a purely imaginary number?
A. 3 + 0i
B. 0 + 5i
C. 2
D. 1 + 1i
Show Answer & Explanation
Correct Answer: B
A purely imaginary number has no real part and is of the form 0 + bi. Among the options, 0 + 5i is purely imaginary.
Q4
Medium
If z = 3 + 4i, find the modulus of z.
A. 5
B. 7
C. 12
D. 10
Show Answer & Explanation
Correct Answer: A
The modulus of a complex number z = a + bi is given by √(a² + b²). Here, √(3² + 4²) = √(9 + 16) = √25 = 5.
Q5
Medium
For z = -2 + 5i, find the conjugate of z.
A. -2 - 5i
B. 2 - 5i
C. -2 + 5i
D. 2 + 5i
Show Answer & Explanation
Correct Answer: A
The conjugate of a complex number z = a + bi is given by a - bi. Therefore, the conjugate is -2 - 5i.
Q6
Medium
If z = 3 + 4i, find the real part of z.
A. 3
B. 4
C. 7
D. 1
Show Answer & Explanation
Correct Answer: A
The real part of a complex number z = a + bi is simply a. Here, the real part is 3.
Q7
Medium
What is the real part of the complex number z = 4 - 7i?
A. 4
B. -7
C. 1
D. -4
Show Answer & Explanation
Correct Answer: A
The real part of a complex number z = a + bi is a. Here, the real part is 4.
Q8
Hard
If z = x + yi, where x and y are real numbers, what is the condition that z must satisfy to have an argument of 45 degrees?
A. x = y
B. x = -y
C. x > y
D. x < y
Show Answer & Explanation
Correct Answer: A
The argument of a complex number z = x + yi is given by tan^-1(y/x). For an argument of 45 degrees, y/x = 1, which means x = y.
Q9
Hard
If z = re^(iθ), and r = 2, what is the value of z^4?
A. 16e^(i4θ)
B. 8e^(i2θ)
C. 4e^(i2θ)
D. 2e^(i4θ)
Show Answer & Explanation
Correct Answer: A
Using the property of exponents for complex numbers, (re^(iθ))^4 = r^4 e^(i4θ) = 2^4 e^(i4θ) = 16e^(i4θ).
Q10
Hard
The equation z^4 + 1 = 0 has how many distinct complex roots?
A. 2
B. 4
C. 8
D. 6
Show Answer & Explanation
Correct Answer: B
The equation z^4 + 1 = 0 can be rewritten as z^4 = -1. The distinct roots are given by z = e^(i(π/4 + kπ/2)) for k = 0, 1, 2, 3, thus yielding 4 distinct roots.

Showing 10 of 1613 questions. Start a quiz to practice all questions with scoring and timer.

Practice All 1613 Questions →

More Mathematics Chapters

1 Sets Relations and Functions
1652 Qs →
2 Matrices and Determinants
1781 Qs →
3 Permutations and Combinations
1645 Qs →
4 Limits Continuity and Differentiability
1661 Qs →
5 Integral Calculus
1623 Qs →
6 Differential Equations
2044 Qs →
7 Coordinate Geometry
1290 Qs →
8 Vector Algebra and 3D Geometry
1678 Qs →

Other JEE Subjects

⚡ Physics → ⚗️ Chemistry →

Complex Numbers — JEE Mathematics Practice Questions Online

This page contains 1613 practice MCQs for the chapter Complex Numbers in JEE Mathematics. The questions are organized by difficulty — 375 easy, 712 medium, 526 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 6 topics, giving you comprehensive coverage of the entire chapter.