Embibe Experts Solutions for Chapter: Complex Numbers, Exercise 1: AP EAPCET 2021 (19-Aug Afternoon)

If ${\left(\frac{1+i}{1-i}\right)}^m=1$, then $m$ can not be equal to

If $a>0$ and $z=x+iy$, then ${\log }_{{\cos }^2\theta }|z-a|>{\log }_{{\cos }^2\theta }|z-ai|,(\theta \in R)$ implies

If ${\left|z_1+z_2\right|}^2={\left|z_1\right|}^2+{\left|z_2\right|}^2$, where $z_1$ and $z_2$ are two complex numbers, then

What is the value of $(1-i\sqrt{3}{)}^9=$

${\left(\frac{\sqrt{6}-\sqrt{2}}{4}+\frac{\sqrt{6}+\sqrt{2}}{4}i\right)}^{2020}=$

If $1,{\alpha }_1,{\alpha }_2,{\alpha }_3,{\alpha }_4$ are the roots of $z^5-1=0$ and $\omega$ is a cube root of unity then $(\omega -1)\left(\omega -{\alpha }_1\right)\left(\omega -{\alpha }_2\right)\left(\omega -{\alpha }_3\right)\left(\omega -{\alpha }_4\right)+\omega$ is equal to

If $\alpha$ and $\beta$ are the roots of the quadratic equation $x^2+x+1=0$, then the equation whose roots are ${\alpha }^{2021},{\beta }^{2021}$ is given by ______

If $|z-2|=|z-1|$, where $z$ is a complex number, then locus of $z$ is a straight line