Argument of complex number frac{{13 - 5i}}{{4

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4-1.Complex numbers

easy

The argument of the complex number $\frac{{13 - 5i}}{{4 - 9i}}$is

$\frac{\pi }{3}$

$\frac{\pi }{4}$

$\frac{\pi }{5}$

$\frac{\pi }{6}$

Solution

(b)$arg\left( {\frac{{13 – 5i}}{{4 – 9i}}} \right) = arg(13 – 5i) – arg(4 – 9i)$
$ = – {\tan ^{ – 1}}\left( {\frac{5}{{13}}} \right) + {\tan ^{ – 1}}\frac{9}{4} = \frac{\pi }{4}$

Standard 11

Mathematics

Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$

normal

If $|z – 25i| \le 15$, then $|\max .amp(z) – \min .amp(z)| = $

hard

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex number $z$ satisfying the equation $w – \overline {w}z = k\left( {1 – z} \right)$ , for some real number $k$, is

hard

(JEE MAIN-2014)

If ${Z_1} \ne 0$ and $Z_2$ be two complex numbers such that $\frac{{{Z_2}}}{{{Z_1}}}$ is a purely imaginary number, then $\left| {\frac{{2{Z_1} + 3{Z_2}}}{{2{Z_1} – 3{Z_2}}}} \right|$ is equal to

hard

(JEE MAIN-2013)

If $z = \frac{{ – 2}}{{1 + \sqrt 3 \,i}}$ then the value of $arg\,(z)$ is

easy

The argument of the complex number $\frac{{13 - 5i}}{{4 - 9i}}$is

Solution

Similar Questions

Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$

If $|z – 25i| \le 15$, then $|\max .amp(z) – \min .amp(z)| = $

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex number $z$ satisfying the equation $w – \overline {w}z = k\left( {1 – z} \right)$ , for some real number $k$, is

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If $z = \frac{{ – 2}}{{1 + \sqrt 3 \,i}}$ then the value of $arg\,(z)$ is

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