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Previous year question hub

Complex Numbers - Algebra - Mathematics Previous Year Questions

Practice Complex Numbers - Algebra - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

4Papers
4Years
4Questions
1Topics

Complex Numbers question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Complex Numbers. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Not classified 4 100%

Question type distribution

MCQ, numerical, multiple-select and other formats found in these papers.

Multiple Choices 4 100%

Subject weightage

Top subjects by unique question coverage.

Mathematics
4 Qs

Most asked topics

Top topics across the included previous year papers.

Algebra
4 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Complex Numbers
4 Qs

Paper coverage

Question coverage for the most populated papers. Every active PYP paper remains listed below.

IAT IISER 2025
1 Qs
IAT IISER 2024
1 Qs
IAT IISER 2022
1 Qs
IAT IISER 2020
1 Qs

Included previous year papers

Newest papers appear first. Sort by year, question coverage or name.

PaperYear / sessionQuestions in this viewOpen
IAT IISER 202520251View paper
IAT IISER 202420241View paper
IAT IISER 202220221View paper
IAT IISER 202020201View paper

All Complex Numbers previous year questions

Practice every matching question in batches of 20, with every available option.

1
2020 · Mathematics · Algebra · Complex Numbers
IAT IISER 2020
Let $a, b$ be nonzero real numbers. If $p(x)=x^n+c_{n-1} x^{n-1}+\cdots+c_0$, where $c_{n-1}, \ldots, c_0$ are integers and $n \geq 3$, then which of the following statements is correct?
A
If $a+i b$ is a root of $p(x)$, then $n$ must be even.
B
If $a$ is a root of $p(x)$, then $n$ must be odd.
C
If $a+i b$ is a root of $p(x)$, then $(a+i b)^2$ can never be a root of $p(x)$.
D
If $a$ is a root of $p(x)$, then $a$ must be an integer.
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2
2022 · Mathematics · Algebra · Complex Numbers
IAT IISER 2022

    Let $\omega$ be a complex root of the quadratic polynomial $x^2+x+1$. The value of

    $$\left(\omega+\frac{1}{\omega}\right) \cdot\left(\omega^2+\frac{1}{\omega^2}\right) \cdots\left(\omega^{100}+\frac{1}{\omega^{100}}\right)$$

    is

A
$2^{33}$
B
$2^{31}$
C
$-2^{33}$
D
$-2^{31}$
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3
2024 · Mathematics · Algebra · Complex Numbers
IAT IISER 2024

Consider the following subset of the $X Y$-plane.

$$S=\left\{\left(|z-\mathrm{i} z|,|z|^2\right): \quad z \text { is a complex number }\right\}$$

Which one of the following statements is correct?

A
$S$ is a circle
B
$S$ is a parabola.
C
$S$ is an ellipse but not a circle
D
$S$ is a hyperbola.
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4
2025 · Mathematics · Algebra · Complex Numbers
IAT IISER 2025

Let $z_1, z_2$, and $z_3$ be complex numbers satisfying the following conditions

$$2=\left|2 z_1\right|=\left|z_2-1\right|=\left|z_3+1\right|=\left|\frac{1}{z_1}+\frac{1}{z_2-1}+\frac{1}{z_3+1}\right| .$$

What is the value of $\left|4 z_1+z_2+z_3\right|$ ?

A

8

B

4

C

$\frac{1}{4}$

D

$\frac{1}{8}$

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