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Previous year question hub

Complex Numbers and Analytic Functions - Complex variables - Engineering Sciences Previous Year Questions

Practice Complex Numbers and Analytic Functions - Complex variables - Engineering Sciences previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
20Years
26Questions
1Topics

Complex Numbers and Analytic Functions question pattern

Every graph below is calculated only from this selection.

Questions by year

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

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 19 73.1%
Easy 6 23.1%
Hard 1 3.8%

Question type distribution

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

MCQ 23 88.5%
Numerical Answer Type (NAT) 3 11.5%

Subject weightage

Top subjects by unique question coverage.

Engineering Sciences
26 Qs

Most asked topics

Top topics across the included previous year papers.

Complex variables
26 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Complex Numbers and Analytic Functions
26 Qs

Paper coverage

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

Engineering Sciences (XE) 2026
1 Qs
Engineering Sciences (XE) 2025
1 Qs
Engineering Sciences (XE) 2024
1 Qs
Engineering Sciences (XE) 2023
1 Qs
Engineering Sciences (XE) 2022
1 Qs
Engineering Sciences (XE) 2021
1 Qs
Engineering Sciences (XE) 2020
1 Qs
Engineering Sciences (XE) 2019
2 Qs
Engineering Sciences (XE) 2018
1 Qs
Engineering Sciences (XE) 2017
1 Qs
Engineering Sciences (XE) 2016
1 Qs
Engineering Sciences (XE) 2015
1 Qs
Engineering Sciences (XE) 2014
1 Qs
Engineering Sciences (XE) 2013
2 Qs
Engineering Sciences (XE) 2012
1 Qs
Engineering Sciences (XE) 2011
1 Qs
Engineering Sciences (XE) 2010
1 Qs
Engineering Sciences (XE) 2009
1 Qs
Engineering Sciences (XE) 2008
3 Qs
Engineering Sciences (XE) 2007
3 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
Engineering Sciences (XE) 202620261View paper
Engineering Sciences (XE) 202520251View paper
Engineering Sciences (XE) 202420241View paper
Engineering Sciences (XE) 202320231View paper
Engineering Sciences (XE) 202220221View paper
Engineering Sciences (XE) 202120211View paper
Engineering Sciences (XE) 202020201View paper
Engineering Sciences (XE) 201920192View paper
Engineering Sciences (XE) 201820181View paper
Engineering Sciences (XE) 201720171View paper
Engineering Sciences (XE) 201620161View paper
Engineering Sciences (XE) 201520151View paper
Engineering Sciences (XE) 201420141View paper
Engineering Sciences (XE) 201320132View paper
Engineering Sciences (XE) 201220121View paper
Engineering Sciences (XE) 201120111View paper
Engineering Sciences (XE) 201020101View paper
Engineering Sciences (XE) 200920091View paper
Engineering Sciences (XE) 200820083View paper
Engineering Sciences (XE) 200720073View paper

All Complex Numbers and Analytic Functions previous year questions

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

1
2007 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2007
The value of the contour integral \( \oint_{|z|=1} \frac{\cosh z}{4z^2 + 1} dz \) is equal to
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2
2007 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2007
Let \( f(z) = \frac{1}{1 - z^2} \). The coefficient of \( \frac{1}{z - 1} \) in the Laurent expansion of \( f(z) \) about \( z = 1 \) is
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3
2007 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2007
Let \( f(x+iy)=u(x,y)+iv(x,y) \) be an analytic function defined on the complex plane satisfying \( 2u^2 + 3v^2 = 1 \). Then
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4
2008 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2008
If \(f(z) = u + iv\) is an analytic function and \(u - v = (x - y)^3 + kxy(x - y)\), then \(k\) is
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5
2008 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2008
If \( f(z) = y(1 + x^2) + x^2 + i(y^2 + 2y)x \) is differentiable at a point \( z = z_0 \), then \( f'(z_0) \) is
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6
2008 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2008
The value of the integral \( \oint_{|z|=3} \frac{e^{1/z}}{(z-1)^2} dz \) is
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7
2009 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2009
If a complex function \(f(z)=u(x,y)+i v(x,y)\) is analytic, then
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8
2010 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2010
The residue of the function \( f(z) = \frac{\sin^4 z}{(z + \pi/4)^3} \) at \( z = -\pi/4 \) is
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9
2011 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2011
The integral $\oint_C \frac{z^3 e^z}{(z-1)^3} dz$ along the curve $C: |z| = \frac{\pi}{2}$, oriented counter-clockwise, equals
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10
2012 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2012
Consider two functions \( f(z) = |z| \) and \( g(z) = \bar{z} \) (conjugate of \( z \)). Using Cauchy-Riemann conditions, choose the correct answer
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11
2013 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2013
Consider the function \(f(z) = z^2 \bar{z}, \; z \in \mathbb{C}\). At \(z = 0\), the function \(f\)
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12
2013 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2013
The integral \(\oint_{C} \frac{(z+4)}{(z+1)(z-2)^{3}} d z\) along the contour \(C:|z-(1+i)|=2\), oriented anti-clockwise, is equal to
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13
2014 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2014
At z = 0, the complex function f(z) = z|z|²
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14
2015 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2015
For a complex number \(k\) and a complex variable \(z\), the complex function \((z + k)^2\) is analytic
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15
2016 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2016
The Laurent series of \( f(z) = 1/(z^3 - z^4) \) with center at \( z = 0 \) in the region \( |z| > 1 \) is
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16
2017 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2017
Let
\[I = \int_{0}^{1} \frac{1}{1 + t} \, dt + \frac{\pi i}{2} \int_{0}^{1} \frac{e^{\frac{\pi i t}{2}}}{1 + e^{\frac{\pi i t}{2}}} \, dt - i \int_{0}^{1} \frac{1}{1 + i t} \, dt,\]
where \(t\) is a real variable and \(i = \sqrt{-1}\). The value of \(I\) is ______________.
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17
2018 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2018
Let \( \mathbb{C} \) denote the set of complex numbers and \( i^2 = -1 \). Let \( \gamma \) be the simple positively oriented circle \( |z| = 1 \) and \( S = \{ z \in \mathbb{C} \mid 0 < |z| < 2 \} \). If \( f : S \to \mathbb{C} \) is analytic in \( S \) and is given by \( f(z) = \frac{1}{8z^2} + \frac{7}{2z} + \sum_{n=0}^{\infty} a_n z^n, \ z \in S \), then the value of the contour integral \( \frac{1}{\pi i} \oint_{\gamma} \left( \frac{e^z}{\cos z} + f(z) \right) dz \) is
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18
2019 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2019
Let \(f(z) = \bar{z} e^{-|z|^2}\), where \(\bar{z}\) is the complex conjugate of \(z\). Then, it is differentiable on
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19
2019 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2019
Let \( I = \frac{10^5 i}{2\pi} \oint_{\gamma} \frac{dz}{(z-4)(z^2-1)} \), where \( i = \sqrt{-1} \) and \( \gamma \) is the circle \( |z| = 2 \) oriented counter clockwise. Then, the value of \( I \) rounded off to one decimal place is ______.
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20
2020 · Engineering Sciences · Complex variables · Complex Numbers and Analytic Functions
Engineering Sciences (XE) 2020
Let \( z \) be a complex number. Then the series \( \sum_{n=0}^{\infty} \frac{z^{2n}}{(2n)!} \)
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Showing 20 of 26 questions