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The polar form of the complex number $(i^{25})^{3}$ is

\[\begin{array}{1 1}(1)\cos\frac{\pi}{2}+i\sin\frac{\pi}{2}&(2)\cos\pi+i\sin\pi\\(3)\cos\pi-i\sin\pi&(4)\cos\frac{\pi}{2}-i\sin\frac{\pi}{2}\end{array}\]

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$(i^{25})^{3} =i^{75}= i^{72}.i^3=(i^4)^{18}.i^3$
$\qquad= 1 \times i^2.i=-i$
$(i^{25})^{3} =-i $
$\qquad= \cos \large\frac{\pi}{2} $$-i \sin \large\frac{\pi}{2}$
Hence 4 is the correct answer.
answered May 14, 2014 by meena.p
 

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