The real part of $e^{(3+4i)x}$ is

Important Questions on Complex Numbers

HARD

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2020>Q 2

If $z=x-iy$ and $z^{\frac{1}{3}}=p+iq$, then $\frac{1}{p^2+q^2}\left(\frac{x}{p}+\frac{y}{q}\right)$ is equal to

MEDIUM

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2020>Q 3

Let $z=x+iy$ be a complex number such that $|z+i|=2$. Then the locus of $z$ is a circle whose centre and radius are

MEDIUM

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2020>Q 4

If $2+i$ is a root of $x^2-4x+c=0,$ where $c$ is a real number, then the value of $c$ is

HARD

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2020>Q 5

The principal argument of the complex number $z=\frac{1+\sin \pi -i\cos \pi }{1+\sin \pi +i\cos \pi }$ is

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2019>Q 6

If $z$ is a normal root of $\sqrt[7]{-1}$ then $z^{85}+z^{142}+z^{191}$ is.

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2019>Q 7

If $z_1=5y^2-3-8ix,z_2=4y^2-16i$ and $z_1={\overline{z}}_2$ then $z=x+iy$ is equal to

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2019>Q 8

The value of $(1+i{)}^5\times (1-i{)}^5$ is

EASY

KEAM

IMPORTANT

EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 14 - Complex Numbers>KEAM 2018>Q 9

The value of ${\left(i^{18}+{\left(\frac{1}{i}\right)}^{25}\right)}^3$ is equal to