Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: Exercise 1

If $z=i \left(i+\sqrt{2}\right)$, then the value of $z^4+4z^3+6z^2+4z$ is

If $\left|z_1\right|=\left|z_2\right|$ and $\arg \left(\frac{z_1}{z_2}\right)=\pi$, then $z_1+z_2$ is equal to

Let $S=\left\{z\in C : z\left(i{z}_1-1\right)=z_1+1, \left|z_1\right|<1\right\}$. Then, for all $z\in S,$ which one of the following is always true?

The complex number $z$ satisfying $|z+\overline{z}|+|z-\overline{z}|=2$ and $|iz-1|+|z-i|=2$ is/are

If a complex number $z$ lies on a circle of radius $3$ and centre at $z_0=0$ then the complex number $\left(-3+9z\right)$ lies on a circle of radius

$z_1,z_2,z_3$ are three points lying on the circle $\left|z\right|=1$, then maximum value of ${\left|z_1-z_2\right|}^2+{\left|z_2-z_3\right|}^2+{\left|z_3-z_1\right|}^2$ is equal to -

Given that the equation $z^2+(a+ib)z+c+id=0$ where $a, b, c, d$ are non-zero, has a real root then

It is given that the equation $|z{|}^2-2iz+2\alpha (\lambda +i)=0$ possesses a solution for all $\alpha \in R,$ then the number of integral value(s) of ' $\lambda$ ' for which it is true is