Amplitude of frac{{1 + √ 3 ,i}}{{√ 3 + i}} is

English

Gujarati

Hindi

4-1.Complex numbers

easy

The amplitude of $\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 + i}}$ is

$\frac{\pi }{6}$

$ - \frac{\pi }{6}$

$\frac{\pi }{3}$

None of these

Solution

(a)$amp\,\left( {\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 + i}}} \right)$$ = amp(1 + \sqrt 3 \,i\,) – amp(\sqrt 3 + i)$
$ = \frac{\pi }{3} – \frac{\pi }{6} = \frac{\pi }{6}$.

Standard 11

Mathematics

If $z$ is a complex number, then the minimum value of $|z| + |z – 1|$ is

medium

The solution of the equation $|z| – z = 1 + 2i$ is

medium

If ${z_1}$ and ${z_2}$ are any two complex numbers then $|{z_1} + {z_2}{|^2}$ $ + |{z_1} – {z_2}{|^2}$ is equal to

easy

Number of complex numbers $z$ such that $\left| z \right| + z – 3\bar z = 0$ is equal to

normal

If $z $ is a complex number of unit modulus and argument $\theta$, then ${\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)$ equals.

medium

(JEE MAIN-2013)

The amplitude of $\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 + i}}$ is

Solution

Similar Questions

If $z$ is a complex number, then the minimum value of $|z| + |z – 1|$ is

The solution of the equation $|z| – z = 1 + 2i$ is

If ${z_1}$ and ${z_2}$ are any two complex numbers then $|{z_1} + {z_2}{|^2}$ $ + |{z_1} – {z_2}{|^2}$ is equal to

Number of complex numbers $z$ such that $\left| z \right| + z – 3\bar z = 0$ is equal to

If $z $ is a complex number of unit modulus and argument $\theta$, then ${\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)$ equals.

Start a Free Trial Now