Embibe Experts Solutions for Exercise 6: EXERCISE

If $z_1,z_2,z_3,z_4$ are the affixes of four points in the Argand plane and $z$ is the affix of a point such that $\left|z-z_1\right|=\left|z-z_2\right|=\left|z-z_3\right|=\left|z-z_4\right|,$ then $z_1,z_2,z_3,z_4$ are

If $A\left(z_1\right)$ and $B\left(z_2\right)$ are two fixed points in the argand plane the locus of point $P\left(z\right)$ satisfying $\left|z-z_1\right|+\left|z-z_2\right|=\left|z_1-z_2\right|$, is

The vertices of a square are $z_1,z_2,z_3$ and $z_4$ taken in the anticlockwise order, then $z_3=$ 

A rectangle is constructed in the complex plane with its sides parallel to the axes and its centre is situated at the origin. If one of the vertices of the rectangle is $a+ib\sqrt{3}$, then find the area of rectangle.

Locus of the point $z$ satisfying the equation $\left|iz-1\right|+\left|z-i\right|=2$ is

If $z=x+iy$ and $\arg \left(\frac{z-2}{z+2}\right)=\frac{\mathrm{\pi }}{6}$, then find the locus of $z$.

Simplify : $i\log \left(\frac{x-i}{x+i}\right)$.

Find the set of values of $K$ for which the equation $z\overline{z}+\left(-3+4i\right)\overline{z}-\left(3+4i\right)z+K=0$ represents a circle.