Complex Numbers
COMEDK / Mathematics / Algebra / 23 questions
MathematicsAlgebra23 PYQs
Practice 23 COMEDK Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
23
PYQs on Page
Mathematics / Algebra
2020-2026
Year Range
Based on indexed question metadata
16
Last 5 Years
2022-2026
23
Last 10 Years
2017-2026
Recent Year Trend
2021
2022
2023
2024
2025
2026Latest year
20214 max PYQs/year2026
Question Types
23PYQs
MCQ100%
Difficulty Mix
#1 Unknown23
16 in last 5 years23 in last 10 years
Complex Numbers Questions
Showing 23 of 23 questions on this page.
1Complex Numbers
\(\text { The conjugate of } z=\frac{(\mathbf{4}+\boldsymbol{i})(\mathbf{1}-\boldsymbol{i})}{(\mathbf{1}+\boldsymbol{i})(\mathbf{2}-\boldsymbol{i})}\)
MCQ+1 / -02026
2Complex Numbers
The conjugate of the multiplicative inverse of the complex number $\boldsymbol{z}=\frac{\mathbf{1}+\mathbf{7} \boldsymbol{i}}{\mathbf{3}+\boldsymbol{i}}$ is:
MCQ+1 / -02026
3Complex Numbers
If $\frac{x-1}{3+i}+\frac{y-1}{3-i}=i$ then $(y, x)=$
MCQ+1 / -02025
4Complex Numbers
If $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^5+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^5$, then
MCQ+1 / -02025
5Complex Numbers
Given that $z$ is a real number and $z=\frac{\lambda+4 i}{1+\lambda i}$ where $\lambda \in R$, then the possible value of $\lambda$ is :
MCQ+1 / -02025
6Complex Numbers
The complex number $\frac{1+7 i}{(2-i)^2}$ lies in
MCQ+1 / -02025
7Complex Numbers
\(\text { The modulus of the following complex number } \frac{1+i}{1-i}-\frac{1-i}{1+i} \text { is }\)
MCQ+1 / -02024
8Complex Numbers
\(\text { If }(1-4 i)^3=a+i b \text { then the value of } \mathrm{a} \text { and } \mathrm{b} \text { is }\)
MCQ+1 / -02024
9Complex Numbers
\(\text { The value of } \frac{i^{1004}+i^{1006}+i^{1008}+i^{1010}+i^{1012}}{i^{510}+i^{508}+i^{506}+i^{504}+i^{502}} \text { is }\)
MCQ+1 / -02024
10Complex Numbers
If the conjugate of \((x+i y)(1-2 i)\) be \(1+i\), then
MCQ+1 / -02023
11Complex Numbers
If \(\left(\frac{3}{2}+i \frac{\sqrt{3}}{2}\right)^{50}=3^{25}(x+i y)\), where \(x\) and \(y\) are real, then the ordered pair \((2 x, 2 y)\) is
MCQ+1 / -02023
12Complex Numbers
If \(i=\sqrt{-1}\) and \(n\) is a positive integer, then \(i^n+i^{n+1}+i^{n+2}+i^{n+3}\) is equal to
MCQ+1 / -02023
13Complex Numbers
If \(z=\sqrt{3}+i\), then the argument of \(z^2 e^{z-i}\) is equal to
MCQ+1 / -02023
14Complex Numbers
\({(i + \sqrt 3 )^{100}} + {(i - \sqrt 3 )^{100}} + {2^{100}}\) is equal to
MCQ+1 / -02022
15Complex Numbers
Evaluate \({\left[ {{i^{22}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}\)
MCQ+1 / -02022
16Complex Numbers
The argument of \({{1 - i\sqrt 3 } \over {1 + i\sqrt 3 }}\) is
MCQ+1 / -02022
17Complex Numbers
If \({(\sqrt 3 + i)^{100}} = {2^{99}}(a + ib)\), then \({a^2} + {b^2}\) is equal to
MCQ+1 / -02021
18Complex Numbers
Evaluate \({\left[ {{i^{18}} + {{\left( {{1 \over i}} \right)}^{25}}} \right]^3}\).
MCQ+1 / -02021
19Complex Numbers
What is the argument of the complex number \({{(1 + i)(2 + i)} \over {3 - i}}\), where \(i = \sqrt { - 1}\) ?
MCQ+1 / -02021
20Complex Numbers
If \(1,\omega ,{\omega ^2}\) are the cube roots of unity, then \((1 + \omega )(1 + {\omega ^2})(1 + {\omega ^4})(1 + {\omega ^8})\) is equal to
MCQ+1 / -02020
21Complex Numbers
The amplitude of \({(1 + i)^5}\) is
MCQ+1 / -02020
22Complex Numbers
The imaginary part of \(i^i\) is
MCQ+1 / -02020
23Complex Numbers
The conjugate of the complex number \({{{{(1 + i)}^2}} \over {1 - i}}\) is
MCQ+1 / -02020
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