Complex Number

Let $C$ be the set of all complex numbers. Let $S_{1}=\left{z\in\,C|\left|z-3-2i\right|^{2}=8\right},$ $S_{2}=z\in\,C|\mathrm{Re}\left(z\right)\geq\,5$and…

If $z$is a complex number satisfying $\left|Re\left(z\right)\right|+\left|Im\left(z\right)\right|=4,$ then $\left|z\right|$ cannot be

If $z$ is a complex number such that $\left|z\right|\geq\,2,$ then the minimum value of $\left|z+\frac{1}{2}\right|$ :

Let$S=\left{z=x+iy:\left|z-1+i\right|\geq\,\left|z\right|,\left|z\right|<2,\left|z+i\right|=\left|z-1\right|\right}$. Then the set of all values of$x$, for which$w=2x+iy\in\,S$for some$y\in\,\mathbb{R}$, is

Let $z\in\,C$ be such that $\left|z\right|<1.$ If $\omega\,=\frac{5+3z}{5\left(1-z\right)},$ then:

The equation $|z-i|=|z-1|,i=\sqrt{-1},$ represents:

For all $z\in\,C$ on the curve $C_{1}:|z|=4$, let the locus of the point $z+\frac{1}{z}$ be the curve $C_{2}$. Then

Let a circle $C$in complex plane pass through the points $z_{1}=3+4i,z_{2}=4+3i$and $z_{3}=5i$. If $z\left(\neq\,z_{1}\right)$is a point on $C$such that the line through$z$ and $z_{1}$is perpendicular to the line…

Let $\mathbb{C}$ be the set of all complex numbers. Let$S_{1}=\left{z\in\,\mathbb{C}:\left|z-2\right|\leq\,1\right}$…

The equation $arg\left(\frac{z-1}{z+1}\right)=\frac{\pi\,}{4}$ represents a circle with:

Let $S_{1},S_{2}$and $S_{3}$ be three sets defined as $S_{1}={z\in\,\mathbb{C}:|z-1|\leq\,\sqrt{2}},$ $S_{2}={z\in\,\mathbb{C}:Re((1-i)z)\geq\,1}$and $S_{3}={z\in\,\mathbb{C}:Im(z)\leq\,1}.$ Then, the set…

If$z$ is a complex number such that$\left|z\right|\leq\,1$, then the minimum value of$\left|z+\frac{1}{2}\left(3+4i\right)\right|$ is: