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The simplified form of { i }^{ n }+{ i }^{ n+1 }+{ i }^{ n+2 }

Question

The simplified form of $i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}$ is

0

1

- 1

i

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The simplified form of

i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}

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Text solutionVerified

Given that:

i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}

= i^{n} + i^{n} \cdot i + i^{n} \cdot i^{2} + i^{n} \cdot i^{3}

, [∵ a^{m + n} = a^{m} \cdot a^{n}]

= i^{n} (1 + i + i^{2} + i^{3})

, take

i^{n}

common

= i^{n} (1 + i - 1 - i)

[∵ i^{2} - 1, i^{3} = i^{2} \cdot i = - i]

= i^{n} (0) = 0

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Question Text	The simplified form of $i^{n} + i^{n + 1} + i^{n + 2} + i^{n + 3}$ is
Answer Type	Text solution:1
Upvotes	150