Complex Number

If $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary, then the minimum value of $|z-(3+3i)|$ is :

If $S=z\in\,C:|z-i|=|z+i|=|z-1|$, then, $n(S)$ is:

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 $\left|z+\frac{1}{2}\right|$ :

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

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

If $z$is a complex number, then the number of common roots of the equation $z^{1985}+z^{100}+1=0$ and $z^{3}+2z^{2}+2z+1=0$, is equal to :

For $a\in\,\mathbb{C}$, let $A={z\in\,\mathbb{C}:\operatorname{Re}\,(a+\overset{\bar{}}{z})>\operatorname{Im}\,(\overset{\bar{}}{a}+z)}$ and $B={z\in\,\mathbb{C}:\operatorname{Re}\,(a+\overset{\bar{}}{z})0$, then the…

If the set$\left{\operatorname{Re}\,\left(\frac{z-\overset{\bar{}}{z}+z\overset{\bar{}}{z}}{2-3z+5\overset{\bar{}}{z}}\right):z\in\,\mathbb{C},\operatorname{Re}\,z=3\right}$isequal to the interval$(\alpha\,,\beta\,]$,…

Let $S=\left{z=x+iy:\frac{2z-3i}{4z+2i}\right$ is a real number $}$. Then which of the following is NOT correct?

Let$w=z\overset{\bar{}}{z}+k_{1}z+k_{2}iz+\lambda\,(1+i),k_{1},k_{2}\in\,\mathbb{R}.$. Let$Re(w)=0$ be the circle$C$of radius $1$ in the firstquadrant touching the line$y=1$ and the$y-$axis. If the curve$Im(w)=0$…

If $\alpha\,$ denotes the number of solutions of$\left|1-i\right|^{x}=2^{x}$ and $\beta\,=\left(\frac{\left|z\right|}{\arg\,\left(z\right)}\right)$,…