How do you write the expression $i ^-18$ in the standard form a+ bi?

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Answer 1 · 2015-02-12T02:07:58

$i^(-18) = -1$
so $a + bi$ becomes
$(-1) + (0)i$

To see that $i^(-18) = -1$
note that
$i^1 = sqrt(-1)$
$i^0 = 1$
$i^-1 =1/(sqrt(-1))$
$i^-2 = 1/(-1) = -1$

$i^-18 = (i^-2)^9 = (-1)^(9) = -1$

How do you write the expression i ^-18i ^-18 in the standard form a+ bi?