If $z _{1}=8 +4i,\ z _{2}=6+4i$ and $arg \left(\dfrac {z-z _{1}}{z-z _{2}}\right)=\dfrac {\pi}{4}$, then $z$ satisfy 

In the complex plane, what is the distance of $4-2i$ from the origin?

In the complex plane, the number 4 + j3 is located in the

If ${z _1}$ and ${z _2}$ are two non-zero complex number such that $\left| {{{{z _1}} \over {{z _2}}}} \right|$ = 2 and $\arg \left( {{z _1}{z _2}} \right) = {{3\pi } \over 2}$ , then ${{\overline {{z _1}} } \over {{z _2}}}$ is equal to 

Given $\left| z \right| =4$ and $Argz=\dfrac{5z}{6}$, then $z$ is

$|z-4| < |z-2|$ represents the region given by?

If $a, b \notin R$, then $|e^{a + ib}| $ is equal to

If $Re(\dfrac{z+2i}{z+4})=0$ then z lies on a circle with center:

The argument of the complex number $\sin \dfrac{{6\pi }}{5} + i\left( {1 + \cos \dfrac{{6\pi }}{5}} \right)$ is 

Let $z,w$ be complex numbers such that $\vec {z}+i\vec {w}=$ and $zw=\pi$ Then $arg\ z$ equals

Let $A$ and $B$ represent $z _{1}$ and $z _{2}$ in the Argand plane and $z _{1},z _{2}$ be the roots of the equation $z^{2}+pz+q=0$ where $p,q$ are complex numbers. If $O$ is the origin $OA=OB$ and $\angle AOB=\alpha$ then $p^{2}=$

Let  $z _ { 1 } , z _ { 2 }$  and  $z _ { 3 }$  represent the vertices  $A, B$  and  $C$  of the triangle  $A B C$  in the argand that  $\left| z _ { 1 } \right| = \left| z _ { 2 } \right| = \left| z _ { 3 } \right| = 5,$  then  $z _ { 1 } \sin 2 A + z _ { 2 } \sin 2 B + z _ { 3 } \sin 2 C = 0.$

If $\sin \frac {6\pi}5+i(1+\cos \frac {6\pi }5)$ then

If Arg $(z + i)\, -$ Arg $(z - i)$ $= \dfrac{\pi}{2}$, then $z$ lies on a ..........

If $\overline { z } $ lies in the third quadrant then $z$ lies in the

Let $z _1$ and $z _2$ are two complex numbers such that $(1-i)z _1=2z _2$ and $arg(z _1z _2)=\dfrac{\pi}{2}$ then $arg(z _2)$ is equals to:

The complex number $\dfrac{1 + 2i}{1 - i}$ lies in which quadrant of the complex plane.

If $arg(z) < 0$, then $arg(-z)-arg(z)=$

Which of the given alternatives represent a point in Argand plane, equidistant from roots of the equation $(z+1)^4= 16z^4$?

A particle starts from a point $z _0= I + i$, where $i
=\sqrt{-1}$ It moves horizontally away from origin by $2$ units and then
vertically away from origin by $3$ units to reach a point$ z _1$. From $z _1$
particle moves $\sqrt{5}$ units in the direction of $2\hat i + \hat j$ and
then it moves through an angle of $\cos e{c^{ - 1}}\sqrt 2 $ in anticlockwise
direction of a circle with centre at origin to reach a point $z _2$ . The arg $z _2$ is given by

The number of solution of $z^2 + \bar{z} = 0$ is

If $z \neq 0$, then $ \overset{100}{\underset{0}{\int}}arg(-|z|)dx =$

The complex no. $\dfrac{1+2i}{1-i}$ lies in which quadrant of the complex plane

If $|z^2-1|=|z^2|+1$, then z lies on?