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# State true or false for the following : If n is a positive integer , then the value of $\;i^{n} + i^{n+1} + i^{n+2} + i^{n+3} \;$ is 0

$(a)\;True\qquad(b)\;false$

Can you answer this question?

Explanation :
True , because $\;i^{n} + i^{n+1} + i^{n+2} + i^{n+3} \;$
$= i^{n}(1 + i + i^{2} + i^{3})$
$= i^{n} (1 + i -1 -i)$
$= I^{n} (0) = 0\;.$
answered Apr 18, 2014 by