How do you simplify $i^{10} + i^{2}$ $i^10+i^2$ ?

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How do you simplify $i^{10} + i^{2}$ $i^10+i^2$ ?

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Answer 1 · 2016-12-03T02:20:32

The expression simplifies to $- 2$ $-2$ .

Explanation:

$i^{10} + i^{2}$ $i^10 + i^2$

Use the exponent rule ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b= x^(ab)$ and change the $i^{10}$ $i^10$ term to an $i^{2}$ $i^2$ term by dividing the exponent $10$ $color(blue)(10)$ by $2 = 5$ $color(red)2=color(magenta)5$ .

$i^{10} = {(i^{2})}^{5}$ $i^color(blue)(10)=(i^color(red)2)^color(magenta)5$

${(i^{2})}^{5} + i^{2}$ $(i^2)^5+i^2$

Recall that $i^{2} = - 1$ $i^2=-1$

${(- 1)}^{5} + (- 1)$ $(-1)^5 +(-1)$

$- 1$ $-1$ raised to an odd power is equal to $- 1$ $-1$ (and btw, $- 1$ $-1$ raised to an even power is equal to $1$ $1$ )

$(- 1) + (- 1) = - 2$ $(-1) +(-1)=-2$

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How do you simplify $i^{10} + i^{2}$ $i^10+i^2$ ?

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