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Previous year question hub

Functions of a complex variable - Complex Analysis - Mathematics Previous Year Questions

Practice Functions of a complex variable - Complex Analysis - Mathematics previous year questions organised from real papers, with year-wise coverage and clear topic navigation.

20Papers
20Years
72Questions
1Topics

Functions of a complex variable question pattern

Every graph below is calculated only from this selection.

Questions by year

Year-wise coverage for Functions of a complex variable. Each bar uses a separate theme-derived color.

Difficulty distribution

How the classified questions are distributed by difficulty.

Medium 50 69.4%
Easy 13 18.1%
Hard 9 12.5%

Question type distribution

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

MCQ 54 75%
Numerical Answer Type (NAT) 10 13.9%
MSQ 8 11.1%

Subject weightage

Top subjects by unique question coverage.

Mathematics
72 Qs

Most asked topics

Top topics across the included previous year papers.

Complex Analysis
72 Qs

Subtopic coverage

Top subtopics inside this exact selection.

Functions of a complex variable
72 Qs

Paper coverage

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

Mathematics (MA) 2026
6 Qs
Mathematics (MA) 2025
4 Qs
Mathematics (MA) 2024
3 Qs
Mathematics (MA) 2023
3 Qs
Mathematics (MA) 2022
4 Qs
Mathematics (MA) 2021
4 Qs
Mathematics (MA) 2020
3 Qs
Mathematics (MA) 2019
3 Qs
Mathematics (MA) 2018
3 Qs
Mathematics (MA) 2017
3 Qs
Mathematics (MA) 2016
2 Qs
Mathematics (MA) 2015
1 Qs
Mathematics (MA) 2014
4 Qs
Mathematics (MA) 2013
6 Qs
Mathematics (MA) 2012
3 Qs
Mathematics (MA) 2011
2 Qs
Mathematics (MA) 2010
3 Qs
Mathematics (MA) 2009
3 Qs
Mathematics (MA) 2008
6 Qs
Mathematics (MA) 2007
6 Qs

Included previous year papers

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

PaperYear / sessionQuestions in this viewOpen
Mathematics (MA) 202620266View paper
Mathematics (MA) 202520254View paper
Mathematics (MA) 202420243View paper
Mathematics (MA) 202320233View paper
Mathematics (MA) 202220224View paper
Mathematics (MA) 202120214View paper
Mathematics (MA) 202020203View paper
Mathematics (MA) 201920193View paper
Mathematics (MA) 201820183View paper
Mathematics (MA) 201720173View paper
Mathematics (MA) 201620162View paper
Mathematics (MA) 201520151View paper
Mathematics (MA) 201420144View paper
Mathematics (MA) 201320136View paper
Mathematics (MA) 201220123View paper
Mathematics (MA) 201120112View paper
Mathematics (MA) 201020103View paper
Mathematics (MA) 200920093View paper
Mathematics (MA) 200820086View paper
Mathematics (MA) 200720076View paper

All Functions of a complex variable previous year questions

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

1
2008 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2008
Let \(S\) be the open unit disk and \(f : S \to \mathbb{C}\) be a real-valued analytic function with \(f(0) = 1\). Then the set \(\{z \in S : f(z) \neq 1\}\) is
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2
2008 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2008
Let \(f\) be a bilinear transformation that maps \(-1\) to \(i\), \(i\) to \(\infty\) and \(-i\) to \(0\). Then \(f(1)\) is equal to
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3
2008 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2008
Let \(T\) be the closed unit disk and \(\partial T\) be the unit circle. Then which one of the following holds for every analytic function \(f: T \to \mathbb{C}\)?
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4
2008 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2008
Let \(S\) be the disk \(|z| < 3\) in the complex plane and let \(f: S \to \mathbb{C}\) be an analytic function such that \(f\left(1 + \frac{\sqrt{2}}{n} i\right) = -\frac{2}{n^2}\) for each natural number \(n\). Then \(f(\sqrt{2})\) is equal to
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5
2008 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2008
Let \(f(z) = \cos z - \frac{\sin z}{z}\) for non-zero \(z \in \mathbb{C}\) and \(f(0) = 0\). Also, let \(g(z) = \sinh z\) for \(z \in \mathbb{C}\). Then \(f(z)\) has a zero at \(z = 0\) of order
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6
2008 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2008
Then \(\frac{g(z)}{zf(z)}\) has a pole at \(z = 0\) of order
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7
2009 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2009
For the function f(z) = sin(1 / cos(1/z)), the point z = 0 is
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8
2009 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2009
Let \(\sum_{n=-\infty}^{\infty} a_n (z+1)^n\) be the Laurent series expansion of \(f(z) = \sin \left( \frac{z}{z+1} \right)\). Then \(a_{-2} =\)
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9
2009 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2009
The residue of \( f \) at the isolated singular point in the upper half plane \( \{z=x+i y \in \mathbb{C}: y>0\} \) is
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10
2010 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2010
Let \( u(x,y) = 2x(1-y) \) for all real \( x \) and \( y \). Then a function \( v(x,y) \), so that \( f(z) = u(x,y) + i v(x,y) \) is analytic, is
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11
2010 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2010
Let \( f(z) \) be analytic on \( D = \{z \in \mathbb{C} : |z-1| < 1\} \) such that \( f(1) = 1 \). If \( f(z) = f(z^2) \) for all \( z \in D \), then which one of the following statements is NOT correct?
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12
2010 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2010
Under the transformation \( w = \sqrt{\frac{1 - iz}{z - i}} \), the region \( D = \{ z \in \mathbb{C} : |z| < 1 \} \) is transformed to
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13
2011 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2011
Which of the following is the imaginary part of a possible value of \(\ln(\sqrt{i})\)?
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14
2011 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2011
Let \( f(z) \) be an entire function such that \( |f(z)| \leq K|z|, \forall z \in \mathbb{C}, \) for some \( K > 0. \) If \( f(1) = i, \) the value of \( f(i) \) is
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15
2012 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2012
The straight lines \(L_1 : x = 0\), \(L_2 : y = 0\) and \(L_3 : x + y = 1\) are mapped by the transformation \(w = z^2\) into the curves \(C_1, C_2\) and \(C_3\) respectively. The angle of intersection between the curves at \(w = 0\) is
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16
2012 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2012
The residue of \( f(z) \) at its pole is equal to 1. Then the value of \( \alpha \) is
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17
2012 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2012
For the value of \( \alpha \) obtained in Q.54, the function \( g(z) \) is not conformal at a point
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18
2013 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2013
The coefficient of \((z - \pi)^2\) in the Taylor series expansion of \(f(z) = \begin{cases} \frac{\sin z}{z - \pi} & \text{if } z \neq \pi \\ -1 & \text{if } z = \pi \end{cases}\) around \(\pi\) is
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19
2013 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2013
Let \(f\) be an entire function on \(\mathbb{C}\) such that \(|f(z)| \le 100 \log|z|\) for each \(z\) with \(|z| \ge 2\). If \(f(i) = 2i\), then \(f(1)\)
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20
2013 · Mathematics · Complex Analysis · Functions of a complex variable
Mathematics (MA) 2013
Let \(f\) be an analytic function on \(\overline{D} = \{z \in \mathbb{C}: |z| \le 1\}\). Assume that \(|f(z)| \le 1\) for each \(z \in \overline{D}\). Then, which of the following is NOT a possible value of \(e^{f'(0)}\)?
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Showing 20 of 72 questions