What is the polar form of the complex number $(i^{25})^{3}$ ?

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Solution

$(i^{25})^{3} = (i^{3})^{25} = i^{75} = (i^{72}) . i^{3} = ((i^{4})^{18}) i^{3}$
we know that $i^{4} = 1$ and $i^{3} = - i$
$(i^{25})^{3} = - i$
$- i = 1 (cos (\frac{- π}{2}) + i sin (\frac{- π}{2}))$

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