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JEE MATHEMATICS MCQ: COMPLEX NUMBERS

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Application +4 | -1
If π2<α<3π2,\frac{\pi }{2} < \alpha < \frac{{3\pi }}{2}, the modulus and argument form of (1+cos⁡2  α)+isin⁡2  α\left( {1 + \cos 2\;\mathrm{\alpha }} \right) + i\sin 2\;\mathrm{\alpha } is
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Correct option: A
−2cos⁡α{cos⁡(π+α)+isin⁡(π+α)}- 2\cos \mathrm{\alpha }\left\{ {\cos \left( {\pi + \alpha } \right) + i\sin \left( {\pi + \alpha } \right)} \right\}
Option A (-2\cos\mathrm{\alpha}\left{\cos \left( {\pi + \alpha } \right) + i\sin \left( {\pi + \alpha } \right)} \right}-2\cos\mathrm{\alpha}\left{\cos \left( {\pi + \alpha } \right) + i\sin \left( {\pi + \alpha } \right)} \right}) is correct because it correctly represents the modulus and argument of the given complex number in the specified range for α\alpha.

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