Express the complex numbers in the form of a + ib:

$i^{- 39}$

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Solution

$i^{- 39}$ $= \frac{1}{i^{39}} = \frac{1}{(i^{2})^{19} . i} = \frac{1}{(- 1)^{19} . i} = \frac{1}{- i} = - \frac{1}{i} \times \frac{i}{i} = \frac{- i}{i^{2}} = \frac{- i}{- i} = i$

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