Amit M Agarwal Solutions for Chapter: Complex Numbers, Exercise 1: Work Book Exercise 4.1

Let $i=\sqrt{-1}$. The product of the real part of the roots of $z^2-z=5-5i$ is

Number of complex numbers $z$ satisfying $z^3=\overline{z}$ is

Number of real solution of the equation, $z^3+iz-1=0$ is

The diagram shows several numbers in the complex plane. The circle is the unit circle centered at the origin. One of these numbers is the reciprocal of $F$, which is

Identify the incorrect statement.

If $z=\left(3+7i\right)\left(p+iq\right),$ where $p, q\in I-\left\{0\right\}$ is purely imaginary, then minimum value of ${\left|z\right|}^2$ is

Consider two complex numbers $\alpha$ and $\beta$ as $\alpha ={\left(\frac{a+bi}{a-bi}\right)}^2+{\left(\frac{a-bi}{a+bi}\right)}^2,$ where $a, b\in R$ and $\beta =\frac{z-1}{z+1},$ where $\left|z\right|=1,$ then

If $z$ is a complex number having the argument $\theta$, $0<\theta <\frac{\mathrm{\pi }}{2}$ and satisfying the equality $\left|z-3i\right|=3$, then, $\cot \theta -\frac{6}{z}$ is equal to