Express the given complex number in the form | vedclass

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(A) Given expression: $i^{-39}$We know that $i^4 = 1$. We can write $-39$ as $4 	imes (-10) + 1$.$i^{-39} = \frac{1}{i^{39}}$$= \frac{1}{i^{4 	imes

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$0+i$

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(A) Given expression: $i^{-39}$We know that $i^4 = 1$. We can write $-39$ as $4 	imes (-10) + 1$.$i^{-39} = \frac{1}{i^{39}}$$= \frac{1}{i^{4 	imes 9 + 3}} = \frac{1}{(i^4)^9 \cdot i^3}$$= \frac{1}{(1)^9 \cdot (-i)} = \frac{1}{-i}$Multiply numerator and denominator by $i$:$= \frac{1 \cdot i}{-i \cdot i} = \frac{i}{-i^2} = \frac{i}{-(-1)} = \frac{i}{1} = i$In the form $a+ib$,this is $0+i$.

Express the given complex number in the form $a+ib$: $i^{-39}$

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