If $a=\cos \theta +i\sin \theta ,$ then $\frac{1+a}{1-a}=$

Important Questions on Complex Numbers and Quadratic Equations

MEDIUM

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 16

The least positive integer $n$ such that ${\left(\frac{2i}{1+i}\right)}^n$ is a positive integer, is

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 17

If $\sqrt{a+ib}=x+iy$ , then possible value of $\sqrt{a-ib}$ is

MEDIUM

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 18

If $(x+iy{)}^{\frac{1}{3}}=a+ib$, then $\frac{x}{a}+\frac{y}{b}=$

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 19

If $x+iy=\frac{3+5i}{7-6i}$, then $y=$

MEDIUM

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 20

A real value of $x$ satisfies the equation $\frac{3-4ix}{3+4ix}=a-ib(a,b\in R),\text{ if }{a}^2+b^2=$

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 21

$\frac{1+2i+3i^2}{1-2i+3i^2}=$

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 22

The value of $(1+i{)}^4+(1-i{)}^4$ is

EASY

Agniveer Vayu

IMPORTANT

Achieve Indian Airforce Agniveer Vayu Mathematics Practice Book>Chapter 4 - Complex Numbers and Quadratic Equations>Exercise>Q 1

If $(1+i)(1+2i)(1+3i)\dots (1+ni)=a+ib$, then $2\times 5\times 10\times \dots \times \left(1+n^2\right)$ is equal to