Class 11 • Maths • Chapter 4
COMPLEX NUMBERS AND QUADRATIC EQUATIONS
True & False Quiz
Real. Imaginary. Complete.
✓True
✗False
25
Questions
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Ch.4
Chapter
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XI
Class
Why True & False for COMPLEX NUMBERS AND QUADRATIC EQUATIONS?
How this format sharpens your conceptual clarity
🔵 Complex numbers complete the number system — every polynomial including x²+1=0 has a solution in ℂ.
✅ T/F tests modulus, argument, conjugate, and powers of i — all exam-critical computations.
🎯 Conjugate of z=a+bi is a−bi (TRUE); −z=−a−bi is different. Also i⁴=1, cycling with period 4.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The imaginary unit \(i\) satisfies \(i^2=-1\).
Q 2
Every real number is also a complex number.
Q 3
The number \(0\) is a purely imaginary number.
Q 4
The complex number \(3-4i\) has real part equal to \(3\).
Q 5
If \(z=5i\), then \(\bar{z}=-5i\).
Q 6
The sum of two complex numbers is always a complex number.
Q 7
The product of two purely imaginary numbers is always negative.
Q 8
The modulus of a complex number is always non-negative.
Q 9
If \(|z|=0\), then \(z=0\).
Q 10
The conjugate of a complex number is unique.
Q 11
If \(z+\bar{z}=0\), then \(z\) is purely imaginary.
Q 12
If \(z\bar{z}=1\), then \(|z|=1\).
Q 13
The equation \(x^2+1=0\) has no real solution.
Q 14
The roots of a quadratic equation with real coefficients and negative discriminant are complex conjugates.
Q 15
If the discriminant of a quadratic equation is zero, then the roots are complex.
Q 16
If \(z\) is a complex number, then \(|z|=|\bar{z}|\).
Q 17
The argument of a complex number is always unique.
Q 18
If \(|z|=1\), then \(z\bar{z}=1\).
Q 19
The quadratic equation \(x^2+2x+5=0\) has real roots.
Q 20
If \(z_1\) and \(z_2\) are complex numbers, then \(|z_1z_2|=|z_1||z_2|\).
Q 21
If \(z\neq0\), then \(\dfrac{1}{z}=\dfrac{\bar{z}}{|z|^2}\).
Q 22
The roots of \(x^2-2\Re(z)x+|z|^2=0\) are always complex conjugates.
Q 23
If the coefficients of a quadratic equation are complex, its roots must be complex.
Q 24
If \(z\) is purely imaginary, then \(z^2\) is a negative real number.
Q 25
The locus of points represented by \(|z-2|=3\) is a circle in the complex plane.
Key Takeaways — COMPLEX NUMBERS AND QUADRATIC EQUATIONS
Core facts for CBSE Boards & JEE
1
i=√(−1), i²=−1, i³=−i, i⁴=1 — powers cycle with period 4.
2
For z=a+bi: |z|=√(a²+b²) and z̄=a−bi (conjugate, NOT negative).
3
z·z̄ = |z|² — always a non-negative real number.
4
Every real number is complex (b=0); ℝ ⊂ ℂ.
5
If discriminant b²−4ac < 0, quadratic has two complex conjugate roots.
6
Polar form: z = r(cosθ + i sinθ), r=|z|, θ=arg(z).