Value of {i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}},,,(n ∈ N) is

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4-1.Complex numbers

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The value of ${i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}}\,,\,(n \in N)$ is

A

$0$

B

$1$

C

$2$

D

None of these

Solution

(a)${i^n} + {i^{n + 1}} + {i^{n + 2}} + {i^{n + 3}} = {i^n}[1 + i + {i^2} + {i^3}]$$ = \,{i^n}[1 + i – 1 – i] = 0$.

Standard 11

Mathematics

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