Find the conjugate of $\frac{1}{(3+4i)}$.

Important Questions on Complex Numbers and Quadratic Equations

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 17

If $z=(1-i)$, find $z^{-1}$.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 18

If $z=(\sqrt{5}+3i)$ and $z^{-1} =\frac{\sqrt{5}}{k}+\frac{3}{k}i$, then the value of $2k$ is

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 19

Prove that $\arg \left(z\right)+\arg \left(\overline{z}\right)=0$.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 20

If $\left|z\right|=6$ and $\arg \left(z\right)=\frac{3\pi }{4}$, find $z$.

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 21

If the principal argument of $(-2i)$ is $\frac{m\mathrm{\pi }}{n}$ then $m+n=$

MEDIUM

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 22

The principal argument of $(1+i\sqrt{3}{)}^2$ is of the form of $\frac{m\mathrm{\pi }}{3}$, then find the value of $m$.

MEDIUM

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 23

The polar form of $-9$ is $m\left(\mathrm{cos\pi }+i\mathrm{sin\pi }\right)$, then $m=$

EASY

11th CBSE

IMPORTANT

Senior Secondary School Mathematics FOR CLASS 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE 5G>Q 24

Write $2i$ in polar form.