Find  $\left|\left(1+i\right)\frac{(2+i)}{(3+i)}\right|$.

Important Questions on Complex Numbers and Quadratic Equations

EASY

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 33

Find the value of $k$, if the principal argument of $(1+i\sqrt{3}{)}^2=\frac{\mathrm{k\pi }}{3}$.

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 34

Where does z lie, if $\left|\frac{z-5i}{z+5i}\right|=1$

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 35

$\sin x+i\cos 2x$ and  $\cos x-i\sin 2x$  are conjugate to each other for:

EASY

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 36

The real value of a for which the expression $\frac{1-i\sin \alpha }{1+2i\sin \alpha }$ is purely real is:

EASY

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 37

If $z=x+ iy$ lies in the third quadrant, then $\frac{\overline{z}}{z}$ also lies in the third quadrant if

EASY

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 38

The value of $(z+3)(\overline{z}+3)$ is equivalent to

EASY

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 39

If ${\left(\frac{1+i}{1-i}\right)}^x=1,$ then

MEDIUM

11th CBSE

IMPORTANT

NCERT Exemplar Mathematics - Class 11>Chapter 5 - Complex Numbers and Quadratic Equations>EXERCISE>Q 40

A real value of $x$ satisfies the equation $\left(\frac{3-4ix}{3+4ix}\right)=\alpha -i\beta ,$ where $\alpha , \beta \in R$ if ${\alpha }^2+{\beta }^2$ is equal to