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Complex Numbers and Quadratic Equations

Get chapter-wise JEE Main & Advanced questions with solutions

Q JEE Main 2021
\text { The sum of the roots of the equation } x+1-2 \log _2\left(3+2^x\right)+2 \log _4\left(10-2^{-x}\right)=0 \text {, is: }
JEE Main Mathematics Medium
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Q JEE MAIN_2021_
Let $z_1$ and $z_2$ be two complex numbers such that arg $\left(z_1-z_2\right)=\frac{\pi}{4}$ and $z_1, z_2$ satisfy the equation $|z-3|=$ $\operatorname{Re}(z)$. Then the imaginary part of...
JEE Main Mathematics Easy
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Q JEE MAIN_2021_
Let $n$ denote the number of solutions of the equation $z^2+3 \bar{z}=0$, where $z$ is a complex number. Then the value of $\sum_{k=0}^{\infty} \frac{1}{n^k}$ is...
JEE Main Mathematics Medium
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Q JEE MAIN_2021
The area of the triangle with vertices A (z), B (iz) and C (z + iz) is :
JEE Main Mathematics Medium
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Q JEE MAIN 2023
Let $\alpha, \beta$ be the roots of the equation $x^2-\sqrt{2} x+2=0$. Then $\alpha^{14}+\beta^{14}$ is equal to
JEE Main Mathematics Medium
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Q JEE MAIN 2025
Let ${{z}_{1}},{{z}_{2}}$ and ${{z}_{3}}$ be three complex numbers on the circle $|z|=1$ with $\arg \left( {{{z}_{1}}} \right)=\frac{{-\pi }}{4},\arg \left( {{{z}_{2}}} \right)=0$ and $...
JEE Main Physics Easy
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