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

Question

Write this in form of $a + b i$ $a + bi$

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Answer 1 · 2018-03-12T15:40:42

$i^{- 39} = i$ $i^(-39) = i$

We know that:

$i^{4} = 1$ $i^4 = 1$

so that in general:

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

Now:

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