If n is a positive integer, then which of following relations is false

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4-1.Complex numbers

easy

If $n$ is a positive integer, then which of the following relations is false

A

${i^{4n}} = 1$

B

${i^{4n - 1}} = i$

C

${i^{4n + 1}} = i$

D

${i^{ - 4n}} = 1$

Solution

(b) We know that ${i^2} = – 1$ ==> ${({i^2})^2} = {( – 1)^2} = 1 \Rightarrow \,\,\,\,{i^{4n}} = {1^n}$
and therefore ${i^{4n – 1}} = – i$.

Standard 11

Mathematics

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