Skip to main content
Yukti Vault

Algebra

Complex Numbers: JEE Main & Advanced PYQs

309 previous year questions on Complex Numbers from JEE Main and JEE Advanced papers, each with its exam and year, an answer and a solution.

Practice this chapter

Questions 301-309 of 309

  1. Let $S_1=\{z\in\mathbb{C}:|z|\le5\}$, $S_2=\left\{z\in\mathbb{C}:\operatorname{Im}\left(\dfrac{z+1-\sqrt{3}i}{1-\sqrt{3}i}\right)\ge0\right\}$ and …
  2. The value of $\left(\dfrac{-1+i\sqrt{3}}{1-i}\right)^{30}$ is :
  3. The region represented by $\{z=x+iy\in\mathbb{C}:|z|-\operatorname{Re}(z)\le1\}$ is also given by the inequality :
  4. Let $z_1,z_2$ and $z_3$ be three complex numbers on the circle $|z|=1$ with $\arg(z_1)=\dfrac{-\pi}{4}$, $\arg(z_2)=0$ and $\arg(z_3)=\dfrac{\pi}{4}$. If …
  5. Let the curve $z(1+i)+\bar{z}(1-i)=4$, $z\in\mathbb{C}$, divide the region $|z-3|\le1$ into two parts of areas $\alpha$ and $\beta$. Then $|\alpha-\beta|$ equals :
  6. Let $\left|\dfrac{\bar{z}-i}{2\bar{z}+i}\right|=\dfrac{1}{3}$, $z\in\mathbb{C}$, be the equation of a circle with center at $C$. If the area of the triangle, whose …
  7. If $\alpha+i\beta$ and $\gamma+i\delta$ are the roots of $x^{2}-(3-2i)x-(2i-2)=0$, $i=\sqrt{-1}$, then $\alpha\gamma+\beta\delta$ is equal to:
  8. Let $O$ be the origin, the point $A$ be $z_1=\sqrt{3}+2\sqrt{2}\,i$, the point $B(z_2)$ be such that $\sqrt{3}\,|z_2|=|z_1|$ and $\arg(z_2)=\arg(z_1)+\frac{\pi}{6}$. Then
  9. If the real part of the complex number $(1-\cos\theta+2i\sin\theta)^{-1}$ is $\dfrac{1}{5}$ for $\theta\in(0,\pi)$, then the value of the integral …

Other chapters