Amplitude of left( {frac{{1 - i}}{{1 + i}}} right) is

English

Gujarati

Hindi

4-1.Complex numbers

easy

Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is

$-\pi\over2$

$\pi\over2$

$\pi\over4$

$\pi\over6$

Solution

(a)$\left( {\frac{{1 – i}}{{1 + i}}} \right) = \frac{{1 – i}}{{1 + i}} \times \frac{{1 – i}}{{1 – i}} = \frac{{{{(1 – i)}^2}}}{2} = \frac{{ – 2i}}{2} = – i$
${\mathop{\rm Im}\nolimits} (z) < 0$, Hence amplitude =$ – \pi /2$.

Standard 11

Mathematics

$\left| {\frac{1}{2}({z_1} + {z_2}) + \sqrt {{z_1}{z_2}} } \right| + \left| {\frac{1}{2}({z_1} + {z_2}) – \sqrt {{z_1}{z_2}} } \right|$ =

easy

The minimum value of $|2z – 1| + |3z – 2|$is

medium

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

easy

Find the modulus and the argument of the complex number $z=-1-i \sqrt{3}$.

medium

If $z$ and $w$ are two complex numbers such that $|zw| = 1$ and $arg(z) -arg(w) =\frac {\pi }{2},$ then

hard

(JEE MAIN-2019)

Amplitude of $\left( {\frac{{1 - i}}{{1 + i}}} \right)$ is

Solution

Similar Questions

$\left| {\frac{1}{2}({z_1} + {z_2}) + \sqrt {{z_1}{z_2}} } \right| + \left| {\frac{1}{2}({z_1} + {z_2}) – \sqrt {{z_1}{z_2}} } \right|$ =

The minimum value of $|2z – 1| + |3z – 2|$is

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

Find the modulus and the argument of the complex number $z=-1-i \sqrt{3}$.

If $z$ and $w$ are two complex numbers such that $|zw| = 1$ and $arg(z) -arg(w) =\frac {\pi }{2},$ then

Start a Free Trial Now