The amplitude of sin 5 π + i ( 1 − cos 5 π )

sin 5 π + i ( 1 − cos 5 π ) = 2 sin 10 π cos 10 π + i 2 sin 2 10 π = 2 sin 10 π ( cos 10 π + i sin 10 π ) For amplitude, tan θ = s i n 10 π π cos 10 π = tan 10 π ⇒ θ = 10 π

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MathematicsComplex NumberGeneral(Modulus,Argument,Conjugate)Medium2 minPYQ_2012

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The amplitude of $sin \frac{π}{5} + i (1 - cos \frac{π}{5})$

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Solution:

$sin \frac{π}{5} + i (1 - cos \frac{π}{5})$ $= 2 sin \frac{π}{10} cos \frac{π}{10} + i 2 sin^{2} \frac{π}{10}$ $= 2 sin \frac{π}{10} (cos \frac{π}{10} + i sin \frac{π}{10})$ For amplitude, $tan θ = \frac{π}{s i n \frac{π}{10}} cos \frac{π}{10} = tan \frac{π}{10}$ $\Rightarrow θ = \frac{π}{10}$

Stream:BITSATSubject:MathematicsTopic:Complex NumberSubtopic:General(Modulus,Argument,Conjugate)

⏱ 2mℹ️ Source: PYQ_2012

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