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If the amplitude of a complex number is $\pi/2$ then the number is

\[\begin{array}{1 1}(1)purely \; imaginary& (2)purely\; real \\(3)0&(4) neither \;real\;nor\;imaginary\end{array}\]

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The complex number purely imaginary
Let the complex number be $z= x+iy$
Given amplitudeof $z= \large\frac{\pi}{2}$
$\tan ^{-1} \bigg( \large\frac{y}{x} \bigg) =\large\frac{\pi}{2}$
$\large\frac{y}{x} $$ =\tan \large\frac{\pi}{2}$
$\large\frac{y}{x} $$ =\infty$
$\quad= \large\frac{1}{0}$
$0=x$
Hence 1 is the correct answer.
answered May 14, 2014 by meena.p
 

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