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How do you simplify $i^{94}$ $i^94$ ?

1 Answer

Feb 7, 2016

$i^{94} = - 1$ $i^94 =- 1$

Explanation:

$94 = 2 \times 47$ $94 = 2xx47$
$\to i^{94} = {(i^{2})}^{47} = {(- 1)}^{47}$ $rarr i^94 = (i^2)^47 = (-1)^47$

${(- 1)}^{47} = {(- 1)}^{46} \times (- 1)$ $(-1)^47 = (-1)^46xx(-1)$

$XXXX = {({(- 1)}^{2})}^{23}) \times (- 1)$ $color(white)("XXXX")=((-1)^2)^23)xx(-1)$

$XXXX = (1^{23}) \times (- 1)$ $color(white)("XXXX")=(1^23)xx(-1)$

$XXXX = 1 \times (- 1)$ $color(white)("XXXX")=1xx(-1)$

$XXXX = - 1$ $color(white)("XXXX")=-1$

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