Complex Numbers

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

The area of the triangle with vertices $P(z),Q(iz)$ and $R(z+iz)$ is

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

Let$P=\left{z\in\,\mathbb{C}:\left|z+2-3i\right|\leq\,1\right}$and$Q=\left{z\in\,\mathbb{C}:z\left(1+i\right)+\overset{\bar{}}{z}\left(1-i\right)\leq\,-8\right}$. Let in$P\cap\,Q,\left|z-3+2i\right|$bemaximum and…

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

Let $\left(z\right)$ represent the principal argument of the complex number $z$. The, $\left|z\right|=3$ and$\arg\,\left(z-1\right)-\arg\,\left(z+1\right)=\frac{\pi\,}{4}$ intersect:

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

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

Let$S_{1}=\left{z_{1}\in\,C:\left|z_{1}-3\right|=\frac{1}{2}\right}$and $S_{2}=\left{z_{2}\in\,C:\left|z_{2}-\left|z_{2}+1\right|\right|=\left|z_{2}+\left|z_{2}-1\right|\right|\right}.$ Then, for $z_{1}\in\,S_{1}$ and…

Let a complex number be $w=1-\sqrt{3}i$. Letanother complex number $z$ be such that $|zw|=1$and $\arg\,\left(z\right)-\arg\,\left(w\right)=\frac{\pi\,}{2}$. Then the area of thetriangle (in sq. units) with vertices…

For $z\in\,\mathbb{C}$if the minimum value of $\left(\left|z-3\sqrt{2}\right|+\left|z-p\sqrt{2}i\right|\right)$is$5\sqrt{2}$, then a value of$p$ is _______.