Complex Numbers

If $Z$ is a complex number such that $|Z| \leq 3$ and $\frac{-\pi}{2} \leq a m p Z \leq \frac{\pi}{2}$, then the area of the region formed by locus of $Z$ is

The locus of the complex number Z such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is

If \(m\) and \(n\) are the least and greatest values of \(|z|\) respectively and \(|z-4+3 i| \leq 1\). Let \(k\) be the least value of \(\frac{x^4+x^2+4}{x}\) on the interval \((0, \infty)\).$ Then \(k=\)

Let $z=x+i y$ be a complex number $(x, y \in R)$. Let $A$ and $B$ be two sets such that $A=\{z:|z| \leq 2\}$ and $B=\{z:(z+2 y)+\bar{z} \geq 4\}$ the area of region $A \cap B$ is

Suppose $z\in\,C$ has argument $\theta\,$ such that $0<\theta\,<\frac{\pi\,}{2}$ and satisfy the equation $|z-3i|=3$,then what is the value of $\cot\,\theta\,-\frac{6}{z}?$

If $Z_1$ and $Z_2$ are conjugate complex numbers. Match the items under the following columns? Options : $\begin{array}{llll}A & B & C & D\end{array}$

If the vertices $A, B$ and $C$ of an isosceles $\triangle A B C$ are respectively $z_1, z_2$ and $z_3$ and if $\angle C=90^{\circ}$, then

If $z_1=10+6 i, z_2=4+6 i$ an $z$ is any complex number such that the argument of $\frac{\left(z-z_1\right)}{\left(z-z_2\right)}$ is $\frac{\pi}{4}$, then

If $\mathrm{z}_1, \mathrm{z}_2, \mathrm{z}_3$ are the vertices of an equilateral triangle and $\mathrm{z}$ is its circum centre, then

Let $A\left(3-i\right),B\left(2+i\right)$ be two points in the Argand plane. If the point $P$ represents the complex number $z=x+iy,$ which satisfies $\left|z-3+i\right|=\left|z-2-i\right|,$ then the locus of the point…

Let $A(3-i), B(2+i)$ be two points in the argand plane. If the point $P$ represents the complex number $z=x+i y$, which satisfies $|z-3+i|=|z-2-i|$, then the locus of the point $P$ is

Let $z=x+i y$ be a complex number with $x, y \in Z$. Then, the area (in sq units) of the rectangle whose vertices are the roots of the equation $\bar{z} \cdot z^3+z \cdot \bar{z}^3=350$ is