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Question
Find the value of the following expression:
i30 + i80 + i120
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Solution
\[\ i^{30} + i^{80} + i^{120} \]
\[ = i^{4 \times 7 + 2} + i^{4 \times 20} + i^{4 \times 30} \]
\[ = \left\{ \left( i^4 \right)^7 \times i^2 \right\} + \left\{ \left( i^4 \right)^{20} \right\} + \left\{ \left( i^4 \right)^{30} \right\}\]
\[ = i^2 + 1 + 1 \left[ \because i^4 = 1 \right]\]
\[ = - 1 + 2 \left[ \because i^2 = - 1 \right] \]
\[ = 1\]
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