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STD 11 - 4.1 complex nubers — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 4.1 complex nubers4 Marks
MCQ
If $n$ is a positive integer, then which of the following relations is false
  • A
    ${i^{4n}} = 1$
  • ✓
    ${i^{4n - 1}} = i$
  • C
    ${i^{4n + 1}} = i$
  • D
    ${i^{ - 4n}} = 1$
✓

Answer

Correct option: B.
${i^{4n - 1}} = i$
b
(b) We know that ${i^2} = - 1$ ==> ${({i^2})^2} = {( - 1)^2} = 1 \Rightarrow \,\,\,\,{i^{4n}} = {1^n}$
and therefore ${i^{4n - 1}} = - i$.

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