Complex Numbers PYQs - Last 5 Years
JEE Main / Mathematics / Algebra / 112 recent questions
MathematicsAlgebra2022-2026
Practice 112 JEE Main Mathematics questions from Complex Numbers. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.
112
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Mathematics / Algebra
2022-2026
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112
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2022-2026
112
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2017-2026
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112PYQs
MCQ77.7%
INTEGER22.3%
Difficulty Mix
#1 Medium95
#2 Hard15
#3 Easy2
112 in last 5 years112 in last 10 years
Last 5 Years Complex Numbers Questions
Showing 12 of 112 filtered questions.
1Complex Numbers
Let the minimum value \(v_{0}\) of \(v=|z|^{2}+|z-3|^{2}+|z-6 i|^{2}, z \in \mathbb{C}\) is attained at \({ }{z}=z_{0}\). Then \(\left|2 z_{0}^{2}-\bar{z}_{0}^{3}+3\right|^{2}+v_{0}^{2}\) is equal to :
MCQ+4 / -12022
2Complex Numbers
Let S be the set of all \((\alpha, \beta), \pi<\alpha, \beta<2 \pi\), for which the complex number \(\frac{1-i \sin \alpha}{1+2 i \sin \alpha}\) is purely imaginary and \(\frac{1+i \cos \beta}{1-2 i \cos \beta}\) is purely real. Let $$Z_{\a...
MCQ+4 / -12022
3Complex Numbers
Let \(A = \left\{ {z \in C:\left| {{{z + 1} \over {z - 1}}} \right| < 1} \right\}\) and \(B = \left\{ {z \in C:\arg \left( {{{z - 1} \over {z + 1}}} \right) = {{2\pi } \over 3}} \right\}\). Then A \(\cap\) B is :
MCQ+4 / -12022
4Complex Numbers
If \({z^2} + z + 1 = 0\), \(z \in C\), then \(\left| {\sum\limits_{n = 1}^{15} {{{\left( {{z^n} + {{( - 1)}^n}{1 \over {{z^n}}}} \right)}^2}} } \right|\) is equal to _________.
INTEGER+4 / -12022
5Complex Numbers
Let O be the origin and A be the point \({z_1} = 1 + 2i\). If B is the point \({z_2}\), \({\mathop{\rm Re}\nolimits} ({z_2}) < 0\), such that OAB is a right angled isosceles triangle with OB as hypotenuse, then which of the following is NOT...
MCQ+4 / -12022
6Complex Numbers
If \(z=x+i y\) satisfies \(|z|-2=0\) and \(|z-i|-|z+5 i|=0\), then :
MCQ+4 / -12022
7Complex Numbers
Let a circle C in complex plane pass through the points \({z_1} = 3 + 4i\), \({z_2} = 4 + 3i\) and \({z_3} = 5i\). If \(z( \ne {z_1})\) is a point on C such that the line through z and z1 is perpendicular to the line through z2 and z3, then...
MCQ+4 / -12022
8Complex Numbers
Let z1 and z2 be two complex numbers such that \({\overline z _1} = i{\overline z _2}\) and \(\arg \left( {{{{z_1}} \over {{{\overline z }_2}}}} \right) = \pi\). Then :
MCQ+4 / -12022
9Complex Numbers
For \(\mathrm{n} \in \mathbf{N}\), let \(\mathrm{S}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-3+2 i|=\frac{\mathrm{n}}{4}\right\}\) and \(\mathrm{T}_{\mathrm{n}}=\left\{z \in \mathbf{C}:|z-2+3 i|=\frac{1}{\mathrm{n}}\right\}\). Then the numbe...
MCQ+4 / -12022
10Complex Numbers
For \(z \in \mathbb{C}\) if the minimum value of \((|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)\) is \(5 \sqrt{2}\), then a value Question: of \(p\) is _____________.
MCQ+4 / -12022
11Complex Numbers
Let \(A = \{ z \in C:1 \le |z - (1 + i)| \le 2\}\)
and \(B = \{ z \in A:|z - (1 - i)| = 1\}\). Then, B :
and \(B = \{ z \in A:|z - (1 - i)| = 1\}\). Then, B :
MCQ+4 / -12022
12Complex Numbers
Let S = {z \(\in\) C : |z \(-\) 3| \(\le\) 1 and z(4 + 3i) + \(\overline z\)(4 \(-\) 3i) \(\le\) 24}. If \(\alpha\) + i\(\beta\) is the point in S which is closest to 4i, then 25(\(\alpha\) + \(\beta\)) is equal to ___________.
INTEGER+4 / -12022