Amit M Agarwal Solutions for Chapter: Complex Numbers, Exercise 4: Work Book Exercise 4.4

The straight line $\left(1+2i\right)z+\left(2i-1\right)\stackrel{-}{z}=10i$ on the complex plane, has intercept on the imaginary axis equal to

If the complex number $z$ satisfies the condition $\left|z\right|\ge 3,$ then the least value of $\left|z+\frac{1}{z}\right|$ is equal to

$z_1=\frac{a}{1-i},z_2=\frac{b}{2+i},z_3=a-bi,$ for $a,b\in R$ and $z_1-z_2=1,$ then the centroid of the triangle formed by the points $z_1,z_2,z_3$ in the argand plane is given by

Let $\lambda \in R$. If the origin and the non-real roots of $2z^2+2z+\lambda =0$ form three vertices of an equilateral triangle in the argand plane, then $\lambda$ is

If $a, b, c$ and $u, v, w$ are complex numbers representing the vertices of two triangles, such that $c=\left(1-r\right)a+rb$ and $w=\left(1-r\right)u+rv.$ When $r$ is a complex number, then the two triangles

On the complex plane, $\mathrm{\Delta }OAP$ and $\mathrm{\Delta }OQR$ are similar and $l\left(OA\right)=1$. If the points $P$ and $Q$ denote the complex numbers $z_1$ and $z_2$, then the complex numbers $z$ denoted by the point $R$ is given by

Intercept made by the circle $z\overline{z}+\overline{\alpha }z+\alpha \overline{z}+r=0$ on the real axis on complex plane, is

The equation of the radical axis of the two circles represented by the equations, $\left|z-2\right|=3$ and $\left|z-2-3i\right|=4$ on the complex plane is