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4-1.Complex numbers
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જો $5 + ix^3y^2$ અને $x^3 + y^2 + 6i$ એ અનુબધ્ધ સંકર સંખ્યાઓ છે અને arg $(x + iy) = \theta $ ,હોય તો ${\tan ^2}\,\theta $ ની કિમત મેળવો
A
$4$
B
$5$
C
$6$
D
$7$
Solution
$x^{3}+y^{2}=5 $ and $ x^{3} y^{2}=-6$
$\Rightarrow \mathrm{t}^{2}-5 \mathrm{t}-6=0$ has roots given by $\mathrm{x}^{3} $ and $ \mathrm{y}^{2}$
or $t=6,-1$
$\Rightarrow x^{3}=-1 $ and $ y^{2}=6$
$ \therefore \arg (\mathrm{x}+\mathrm{iy})=\tan ^{-1}(\pm \sqrt{6}) \text { or } \tan ^{2} \theta=6$
Standard 11
Mathematics
