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The modulus and amplitude of the complex number $[e^{3-i \pi/4}]^{3}$ is respectively

\[\begin{array}{1 1}(1)e^{9},\frac{\pi}{2}&(2)e^{9},\frac{-\pi}{2}\\(3)e^{6},\frac{-3\pi}{4}&(4)e^{9},\frac{-\pi}{4}\end{array}\]

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Let $z= \bigg[ e^{3-1} \large\frac{\pi}{4} \bigg]^3$
$\qquad= e^{3(3-i \large\frac{\pi}{4} )} $
$\qquad= e^9.e^{9-i \large\frac{3 \pi}{4}}$
Modulus of $z=e^9$
Amplitude of $z = -\large\frac{3 \pi}{4}$
Hence 4 is the correct answer.
answered May 14, 2014 by meena.p

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