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NDA Complex Numbers and Quadratic Equations questions with solutions

Complex numbers and their algebra. 35 questions from our 2016–2025 NDA pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Complex Numbers and Quadratic Equations for JEE Main · Complex Numbers and Quadratic Equations for JEE Advanced

NDA 2025

/are correct for non-zero complex numbers z, z1, z2? 1. zbar z=|z|^2 2. arg(z1z2)=arg z1+arg z2 for the principal arguments, always.NDA 2025 Maths · medium
If z=x+iy satisfies |(z-1)/(z+1)|=1, then the locus of z isNDA 2025 Maths · medium
If z+1/z=√2, then z^2024+(1)/(z^2024) equalsNDA 2025 Maths · hard

NDA 2024

If z is a complex number satisfying |z-1|=|z+1|, then the locus of z isNDA 2024 Maths · easy
The conjugate of (1+i)/(1-i) is -i. 2. If |z1|=|z2| then z1=z2.NDA 2024 Maths · easy

NDA 2023

The modulus of the complex number ((1+i)^3/(1-i) isNDA 2023 Maths · medium
The value of ((1+i)/(1-i))^2023 isNDA 2023 Maths · medium
The value of i+i^2+i^3+…+i^2023 isNDA 2023 Maths · hard
The imaginary part of the complex number (2+i)/(1-3i) isNDA 2023 Maths · medium

NDA 2022

The locus of the point z in the Argand plane satisfying |z-3|=|z+3| isNDA 2022 Maths · easy
√(-2)·√(-3)=√6. 2. zbar z=|z|^2 for every complex number z.NDA 2022 Maths · medium

NDA 2021

For any complex number z, |z|^2=zbar z. 2. For any non-zero complex number z, |(z)/(bar z)|=1.NDA 2021 Maths · easy
If z=(√3+i)/(2), then z^101 equalsNDA 2021 Maths · hard

NDA 2020

The number of integers n with 1≤ n≤ 20 for which (1+i)^n is a real number isNDA 2020 Maths · medium
The principal argument of (-1+i)^3 isNDA 2020 Maths · hard
If ω is a complex cube root of unity, then (1-ω+ω^2(1+ω-ω^2 equalsNDA 2020 Maths · medium
For a complex number z: 1. zbar z=|z|^2. 2. |bar z|=|z|.NDA 2020 Maths · easy
If z is a complex number satisfying |z-4/z|=2, then the greatest possible value of |z| isNDA 2020 Maths · hard

NDA 2019

If z+1/z=1, then z^12 equalsNDA 2019 Maths · hard
The complex conjugate of ((2+i)^2/(1+i) isNDA 2019 Maths · medium
If ω is a non-real cube root of unity, then the value of (1+ω)(1+ω^2(1+ω^4(1+ω^8 isNDA 2019 Maths · medium
For every non-zero complex number z, arg z+argbar z=0 (principal arguments). 2. For n>1, the sum of all the nth roots of unity is zero.NDA 2019 Maths · hard

NDA 2018

What is the value of i^2018+i^2019+i^2020+i^2021?NDA 2018 Maths · easy
What is the modulus of (3+4i)/(1-2i)?NDA 2018 Maths · easy
What is the principal argument of the complex number -1+i√3?NDA 2018 Maths · medium
If ω is a complex cube root of unity, what is the value of (1+ω)^6?NDA 2018 Maths · medium
|z1+z2|≤|z1|+|z2| for all complex numbers z1,z2. 2. If z≠0 and z+1/z is real, then |z|=1.NDA 2018 Maths · medium

NDA 2017

The real part of (1)/(2-3i) isNDA 2017 Maths · easy
If z=(3+4i)/(1-2i), then |z| equalsNDA 2017 Maths · easy
The value of Σk=1^6(sin (2kπ)/(7)-icos (2kπ)/(7)) isNDA 2017 Maths · hard
The smallest positive integer n for which ((1+i)/(√2))^n=1 isNDA 2017 Maths · medium

NDA 2016

The square roots of the complex number 3+4i areNDA 2016 Maths · medium
The locus of the point z in the Argand plane satisfying |z-2|=|z+2i| isNDA 2016 Maths · medium
The product of all the sixth roots of unity isNDA 2016 Maths · hard
Let z=x+iy be a non-zero complex number. 1. arg(bar z)=arg(z). 2. |z|=x+y.NDA 2016 Maths · easy