What is the value of $i^-39$ ?

Question

Write this in form of $a + bi$

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Answer 1 · 2018-03-12T15:40:42

$i^(-39) = i$

We know that:

$i^4 = 1$

so that in general:

$i^(4k) = (i^4)^k = 1$ for any $k in ZZ$

Now:

$i^(-39) = i^(-40+1) = i^(-40)i = (i^4)^(-10) i = i$