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Complex Numbers and Quadratic Equations — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsComplex Numbers and Quadratic Equations1 Mark
Question
Express the complex numbers $i^{-39}$ in the form of $a + ib.$
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Answer

$i^{-39}= i^{4 \times -9-3}$
$= (i^4)^{-9} \times i^{-3}$
$=(1)^{-9} \times i^{-3}$
$=\frac {1}{i^3}$
$=\frac {1}{-i} \times \frac {i}{i} $
$= \frac {-i}{i^2} = \frac {-i}{-1} = i$

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