Complex Numbers PYQs - Last 10 Years
MHT CET / Mathematics / Algebra / 70 recent questions
MathematicsAlgebra2017-2026
Practice 70 MHT CET Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
70
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Mathematics / Algebra
2019-2026
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59
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2022-2026
70
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2017-2026
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59 in last 5 years70 in last 10 years
Last 10 Years Complex Numbers Questions
Showing 20 of 70 filtered questions.
1Complex Numbers
The value of \(\frac{\mathrm{i}^{248}+\mathrm{i}^{246}+\mathrm{i}^{244}+\mathrm{i}^{242}+\mathrm{i}^{240}}{\mathrm{i}^{249}+\mathrm{i}^{247}+\mathrm{i}^{245}+\mathrm{i}^{243}+\mathrm{i}^{241}}, (\mathrm{i}=\sqrt{-1})\) is
MCQ+2 / -02023
2Complex Numbers
If \((3 x+2)-(5 y-3) i\) and \((6 x+3)+(2 y-4) i\) are conjugates of each other, then the value of \(\frac{x-y}{x+y}\) is (where \(\left.i=\sqrt{-1}, x, y \in R\right)\)
MCQ+2 / -02023
3Complex Numbers
If \(a > 0\) and \(z=\frac{(1+i)^2}{a+i},(i=\sqrt{-1})\) has magnitude \(\frac{2}{\sqrt{5}}\), then \(\bar{z}\) is equal to
MCQ+2 / -02023
4Complex Numbers
If \(|z-2+i| \leq 2\), then the difference between the greatest and least value of \(|z|\) is ________, \((\mathrm{i}=\sqrt{-1})\)
MCQ+2 / -02023
5Complex Numbers
If \(\mathrm{z}=x+\mathrm{i} y\) and \(\mathrm{z}^{1 / 3}=\mathrm{p}+\mathrm{iq}\), where \(x, y, \mathrm{p}, \mathrm{q} \in \mathrm{R}\) and \(\mathrm{i}=\sqrt{-1}\), then value of \(\left(\frac{x}{\mathrm{p}}+\frac{y}{\mathrm{q}}\right)\)...
MCQ+2 / -02023
6Complex Numbers
If \(x=\frac{5}{1-2 \mathrm{i}}, \mathrm{i}=\sqrt{-1}\), then the value of \(x^3+x^2-x+22\) is
MCQ+2 / -02023
7Complex Numbers
If \(w=\frac{z}{z-\frac{1}{3} i}\) and \(|w|=1, i=\sqrt{-1}\), then \(z\) lies on
MCQ+2 / -02023
8Complex Numbers
The argument of \(\frac{1+i \sqrt{3}}{\sqrt{3}+i}, i=\sqrt{-1}\) is
MCQ+2 / -02023
9Complex Numbers
Let \(z\) be a complex number such that \(|z|+z=3+i, i=\sqrt{-1}\), then \(|z|\) is equal to
MCQ+2 / -02022
10Complex Numbers
The sqaure roots of the complex number \((-5-12 \mathrm{i})\) are
MCQ+2 / -02021
11Complex Numbers
If \(\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}\), then x \(-\) y =
MCQ+2 / -02021
12Complex Numbers
If \(z=x+iy\) satisfies the condition \(|z+1|=1\), then \(z\) lies on the
MCQ+2 / -02021
13Complex Numbers
If amplitude of \((z-2-3 i)\) is \(\frac{3 \pi}{4}\), then locus of \(z\) is (where \(z=x+i y\))
MCQ+2 / -02021
14Complex Numbers
If \(x=1+2 i\), then the value of \(x^3+7 x^2-x+16\) is
MCQ+2 / -02021
15Complex Numbers
If \(\omega\) is the complex cube root of unity, then \(\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2=\)
MCQ+2 / -02021
16Complex Numbers
The complex number with argument \(\frac{5 \pi^{\mathrm{c}}}{6}\) at a distance of 2 units from the origin is
MCQ+2 / -02021
17Complex Numbers
If \(z(2-i)=(3+i)\), then \(z^{38}=\), ( where \(z=x+i y\))
MCQ+2 / -02021
18Complex Numbers
The value of (1 + i)\(^5\) (1 \(-\) i)\(^7\) is
MCQ+2 / -02021
19Complex Numbers
If \(\omega\) is complex cube root of unity and \((1+\omega)^7=A+B\omega\), then values of A and B are, respectively
MCQ+2 / -02021
20Complex Numbers
If $\omega$ is a complex cube root of unity and $A=\left[\begin{array}{ccc}\omega & 0 & 0 \\ 0 & \omega^2 & 0 \\ 0 & 0 & 1\end{array}\right]$ then $A^{-1}=\ldots$
MCQ+2 / -02019