Question

Evaluate i^ -999 . This question is from complex no. class 11

Answer 1

Answer:

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Answer 2

Multiply numerator and denominator with $i^{-1}$

$i^{-999}=i^{-999}\times \frac{i^{-1}}{i^{-1}}\\=\frac{i^{-999+-1}}{i^{-1}}\\=\frac{i^{-1000}}{i^{-1}}\\=\frac{i^{2\times -500}}{i^{-1}}\\=\frac{(i^2)^{-500}}{i^{-1}}\\=\frac{(-1)^{-500}}{i^{-1}}\\=\frac{i}{(-1)^{500}}\\=\frac{i}{1}\\=i$