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Chapter 4  ·  Class XI Mathematics  ·  MCQ Practice

MCQ Practice Arena

Complex Numbers & Quadratic Equations

Navigate the Argand Plane — From i² = −1 to De Moivre's Theorem

📋 50 MCQs ⭐ 50 PYQs ⏱ 60 sec/Q
🚀 Start Practising 📖 Revise Notes First

MCQ Bank Snapshot

50Total MCQs
30Easy
15Medium
5Hard
50PYQs
60 secAvg Time/Q
8Topics
Easy 60% Medium 30% Hard 10%

Why Practise These MCQs?

JEE MainJEE AdvancedCBSEBITSATKVPY

This MCQ set focuses on foundational Complex Numbers concepts heavily aligned with NCERT and JEE Main. Most questions test algebraic operations, modulus, conjugates, powers of i, and quadratic equations with complex roots. Argument and polar form are introduced at a basic level. The set emphasizes speed-based solving and concept clarity, making it ideal for early JEE preparation. PYQs dominate, ensuring strong exam relevance, especially for JEE Main where 1–2 direct questions are common from this level.

Topic-wise MCQ Breakdown

Powers of i5 Q
Modulus & Argument6 Q
Argand Plane & Locus2 Q
Polar Form2 Q
De Moivre's Theorem0 Q
Roots of Unity0 Q
Conjugate Properties6 Q
Algebra of Complex Nos.9 Q
Quadratic Discriminant5 Q
Nature of Roots7 Q

Must-Know Formulae Before You Start

Recall these cold before attempting MCQs — they appear in >70% of questions.

$i²=−1, i³=−i, i⁴=1$
$|z|=√(a²+b²)$
$z·z̄=|z|²$
$[r(cosθ+i sinθ)]ⁿ = rⁿ(cos nθ+i sin nθ)$
$D=b²−4ac (D<0 ⟹ complex roots)$

MCQ Solving Strategy

For powers of i, use i^(4k+r) = iʳ and just find the remainder mod 4. For modulus-argument MCQs, convert to polar form immediately. For locus problems on the Argand plane, replace z = x+iy and separate real and imaginary parts — the locus always reduces to a conic or line. Quadratic MCQs: check the sign of discriminant first.

⚠ Common Traps & Errors

Difficulty Ladder

Work through each rung in order — do not jump to Hard before mastering Easy.

① Easy

Powers of i, modulus calculation, basic arithmetic on a+bi

② Medium

Polar form conversion, argument calculation, quadratic roots

③ Hard

Locus on Argand plane, De Moivre's applications, roots of unity

★ PYQ

JEE Advanced — locus and inequality MCQs; JEE Main — modulus problems

Continue Your Preparation

📖 Chapter Notes Revise concepts & theory 🧠 MCQ Practice Topic-wise Questions 🎯 PYQ Bank Previous year questions ✔️❌ True / False Concept-based True & False questions 📘✔️ Exercises Step by step Solutions to textbook exercises ➡ Next Chapter Linear Inequalities MCQs
🎯 Knowledge Check

Maths — COMPLEX NUMBERS AND QUADRATIC EQUATIONS

50 Questions Class 11 MCQs
1
Find the value of \(i^2\).
(NCERT)
2
The real part of the complex number \(3+5i\) is
(NCERT)
3
The imaginary part of \(7-4i\) is
(NCERT)
4
Which of the following is a purely imaginary number?
(NCERT)
5
Find \(|3+4i|\).
(NCERT)
6
The conjugate of \(2-7i\) is
(NCERT)
7
Evaluate \((1+i)^2\).
(NCERT)
8
If \(z=3-2i\), then \(z+\bar z\) equals
(NCERT)
9
If \(z=5+12i\), then \(|z|^2\) is
(NCERT)
10
Find \(\dfrac{1}{i}\).
(NCERT)
11
Solve \(x^2+1=0\).
(NCERT)
12
The discriminant of \(x^2-4x+5=0\) is
(NCERT)
13
Nature of roots of \(x^2-4x+5=0\) is
(NCERT)
14
Find the roots of \(x^2+4=0\).
(NCERT)
15
If \(\alpha,\beta\) are roots of \(x^2-6x+13=0\), then \(\alpha+\beta\) equals
(NCERT)
16
If \(\alpha,\beta\) are roots of \(x^2-6x+13=0\), then \(\alpha\beta\) equals
(NCERT)
17
The value of \(i^{10}\) is
(JEE Main)
18
Simplify \((2+3i)(2-3i)\).
(JEE Main)
19
If \(z+\frac{1}{z}=4\) and \(z\neq0\), then \(z\) is
(JEE Main)
20
Find the argument of the complex number \(1+i\).
(NCERT)
21
If roots of \(x^2+ax+4=0\) are complex, then \(a\) satisfies
(NCERT)
22
The number of solutions of \(x^2+1=0\) in real numbers is
(NCERT)
23
If \(z=1-i\), then \(\frac{z}{\bar z}\) equals
(JEE Main)
24
The roots of \(x^2+2x+5=0\) are
(NCERT)
25
If \(z=a+bi\) and \(|z|=0\), then
(NCERT)
26
Evaluate \(i^{202}\).
(JEE Main)
27
Which quadratic has roots \(2\pm3i\)?
(JEE Main)
28
If \(\alpha\) is a root of \(x^2+px+q=0\), then the other root is
(NCERT)
29
The imaginary part of \(i(3-2i)\) is
(JEE Main)
30
If roots of \(ax^2+bx+c=0\) are equal, then
(NCERT)
31
Find the value of \((1-i)^3\).
(JEE Main)
32
If \(z\bar z=25\) and \(z=3+4i\), then
(NCERT)
33
Roots of \(x^2-2x+2=0\) lie
(NCERT)
34
The quadratic equation with roots \(\pm i\) is
(NCERT)
35
If \(z\) is purely imaginary, then
(NCERT)
36
Find the nature of roots of \(x^2+4x+8=0\).
(NCERT)
37
The value of \(|1-i|^2\) is
(NCERT)
38
If roots of a quadratic are complex, then its graph cuts
(NCERT)
39
If \(z=2(\cos\theta+i\sin\theta)\), then \(|z|\) is
(JEE Main)
40
The roots of \(x^2+1=0\) are
(NCERT)
41
If \(\alpha,\beta\) are roots of \(x^2+px+q=0\), then \(\alpha^2+\beta^2\) equals
(JEE Main)
42
The value of \((i-1)^4\) is
(JEE Main)
43
If one root of a real quadratic equation is \(2+3i\), the other root is
(NCERT)
44
The discriminant of \(x^2+2x+1=0\) is
(NCERT)
45
Find the roots of \(x^2+2x+1=0\).
(NCERT)
46
If \(|z|=5\) and \(z\) is purely imaginary, then \(z\) is
(JEE Main)
47
The equation whose roots are reciprocals of roots of \(x^2-3x+2=0\) is
(JEE Main)
48
The roots of \(x^2+1=0\) lie on
(NCERT)
49
If \(\alpha,\beta\) are roots of \(x^2-5x+6=0\), then \(\alpha^3+\beta^3\) equals
(JEE Main)
50
The nature of roots of \(x^2-2x+5=0\) is
(NCERT)
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Frequently Asked Questions

A complex number is a number of the form \(z = a + ib\), where \(a, b \in \mathbb{R}\) and \(i = \sqrt{-1}\).

For \(z = a + ib\), the real part is \(\Re(z)=a\) and the imaginary part is \(\Im(z)=b\).

The imaginary unit \(i\) is defined by \(i^2 = -1\).

If \(b=0\), the complex number is purely real; if \(a=0\), it is purely imaginary.

The modulus of \(z=a+ib\) is \(|z|=\sqrt{a^2+b^2}\).

The argument \(\theta\) of \(z=a+ib\) satisfies \(\tan\theta=\frac{b}{a}\), taking the correct quadrant into account.

The principal argument \(\arg z\) lies in the interval \((-\pi,\pi]\).

The conjugate of \(z=a+ib\) is \(\bar z=a-ib\).

It is represented as a point \((a,b)\) or a vector in the Argand plane.

It is a plane in which the x-axis represents real parts and the y-axis represents imaginary parts.

The polar form is \(z=r(\cos\theta+i\sin\theta)\), where \(r=|z|\).

Euler’s form is \(z=re^{i\theta}\).

It represents the distance of the point from the origin.

Conjugation represents reflection across the real axis.

It follows the parallelogram law of vector addition.

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