Question
What is \(i \times i^4 \times i^9 \times i^{16} \times \ldots \times i^{576}\), where \(i=\sqrt{-1}\), equal to?
This question was previously asked in
NDA 2 2026 GAT Question Paper (13-Sep-2026)
The correct answer is
1
The exponents are perfect squares \(1^2, 2^2, \ldots, 24^2\) (since \(24^2=576\)), so the product is \(i^{\sum_{k=1}^{24}k^2}\). Using \(\sum_{k=1}^{24}k^2 = \dfrac{24\cdot25\cdot49}{6}=4900\), and since \(4900\) is divisible by 4, \(i^{4900} = 1\).
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