If $z=\frac{\sqrt{3}+i}{2},$ then the value of $z^{69}$ is

Important Questions on Complex Numbers

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2019>Q 23

If $\omega$ is a complex cube root of unity and $\left(1+\omega \right){}^7=A+B\omega ,$ then $A$ and $B$ are equal to

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2018>Q 24

If $z=e^{\frac{i4\pi }{3}}$$,$ then ${\left(z^{192}+z^{194}\right)}^3$ is equal to

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2018>Q 25

The imaginary part of ${\left(i-\sqrt{3}\right)}^{13}$ is