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4-1.Complex numbers
easy
જો $|{z_1} + {z_2}| = |{z_1} - {z_2}|$, તો ${z_1}$ અને ${z_2}$ ના કોણાંકનો તફાવત મેળવો.
A
$\frac{\pi }{4}$
B
$\frac{\pi }{3}$
C
$\frac{\pi }{2}$
D
$0$
Solution
(c) Squaring the given relations implies that
${x_1}{x_2} + {y_1}{y_2} = 0$
Now $amp\,\,{z_1} – amp\,\,{z_2} = {\tan ^{ – 1}}\frac{{{y_1}}}{{{x_1}}} – {\tan ^{ – 1}}\frac{{{y_2}}}{{{x_2}}}$
$ = {\tan ^{ – 1}}\frac{{\frac{{{y_1}}}{{{x_1}}} – \frac{{{y_2}}}{{{x_2}}}}}{{1 + \frac{{{y_1}{y_2}}}{{{x_1}{x_2}}}}} = {\tan ^{ – 1}}\frac{{{y_1}{x_2} – {y_2}{x_1}}}{{{x_1}{x_2} + {y_1}{y_2}}}$$ = {\tan ^{ – 1}}\infty = \frac{\pi }{2}$.
Standard 11
Mathematics
