यदि sqrt 3 + i = (a + ib)(c + id), तब { | vedclass

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Question

(b) $\sqrt 3  + i = (a + ib)(c + id)$

 $	herefore ac - bd = \sqrt 3 $एवं $ad + bc = 1$

अब  $tan^{-1}$ $\left( {\frac{b}{a}} ig

Vedclass · Accepted Answer

$n\pi + \frac{\pi }{6},n \in I$

Vedclass · Answer

(b) $\sqrt 3  + i = (a + ib)(c + id)$

 $	herefore ac - bd = \sqrt 3 $एवं $ad + bc = 1$

अब  $tan^{-1}$ $\left( {\frac{b}{a}} ight) + {	an ^{ - 1}}\left( {\frac{d}{c}} ight)$ $\begin{array}{l} = {	an ^{ - 1}}\left( {\frac{{\frac{b}{a} + \frac{d}{c}}}{{1 - \frac{b}{a}.\frac{d}{c}}}} ight) = {	an ^{ - 1}}\left( {\frac{{bc + ad}}{{ac - bd}}} ight) = {	an ^{ - 1}}\left( {\frac{1}{{\sqrt 3 }}} ight)\\end{array}$

$ = n\pi  + \frac{\pi }{6},n \in I$

यदि $\sqrt 3 + i = (a + ib)(c + id)$, तब ${\tan ^{ - 1}}\left( {\frac{b}{a}} \right) + $${\tan ^{ - 1}}\left( {\frac{d}{c}} \right)$ का मान है

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