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The value of $\large\frac{1}{i}-\frac{1}{i^2}+\frac{1}{i^3}-\frac{1}{i^4}$ = ?

(A) 0 (B) i (C) -i (D) 1

1 Answer

$i^2=-1,\:\:i^3=-i\:\:and\:\:i^4=1$
$\therefore\:\:\large\frac{1}{i}-\frac{1}{i^2}+\frac{1}{i^3}-\frac{1}{i^4}$
$=\large\frac{1}{i}+$$1-\large\frac{1}{i}-$$1=0$
answered Jul 24, 2013 by rvidyagovindarajan_1
 

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