How do you simplify $i^100$ ?

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Answer 1 · 2018-04-25T17:51:17

$i^100=1$

$i^100=(i^2)^50$

From the fact that $i^2=-1,$ we get

$(-1)^50=1$ as $-1$ raised to any even power is $1.$

Alternatively, we can rewrite in trigonometric form and then in the form $re^(itheta)$ :

$i=cos(pi/2)+isin(pi/2)$

$=e^(ipi/2)$

Raise the exponential to the power of $100:$

$(e^(ipi/2))^100=e^(50pi)$

$=cos(50pi)+isin(50pi)$

$=cos2pi+isin2pi$

$cos2pi=1, sin2pi=0$

so we get

$=1$

Answer 2 · 2018-04-25T17:55:06

$i^100=1$

$i^100=(i^2)^50=(-1)^50=1$

$(-a)^n=a^n$ , where n is an even number.

How do you simplify i^100i^100?