Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 2: Exercise-2

$x^2+x+1$ is a factor of $a{x}^3+b{x}^2+cx+d=0$, then the real root of above equation is $(a, b, c, d\in R)$

The locus of equation $Arg\left(\frac{z-1-2i}{z+3+i}\right)=\frac{\pi }{3}$ represents part of circle in which

The equation $|z-i|+|z+i|=k, k>0,$ can represent

If $\left|z_1\right|=\left|z_2\right|=\left|z_3\right|=1$ and $z_1, z_2, z_3$ are represented by the vertices of an equilateral triangle then

If $\alpha , \beta , \gamma$ are distinct roots of $x^3-3x^2+3x+7=0$ and $\omega$ is non-real cube root of unity, then the value of $\frac{\alpha -1}{\beta -1}+\frac{\beta -1}{\gamma -1}+\frac{\gamma -1}{\alpha -1}$ can be equal to

If $z$ is a complex number then the equation $z^2+z\left|z\right|+\left|z^2\right|=0$ is satisfied by ($\omega$ and ${\omega }^2$ are imaginary cube roots of unity).

If $\alpha$ is imaginary $n^{\mathrm{th}}, \left(n\ge 3\right)$ root of unity. Which of the following is/are true.

Which of the following is true?