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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 ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^x} = 1,$ then
  • ✓
    $x = 4n$, where $n$ is any positive integer
  • B
    $x = 2n$, where $n$ is any positive integer
  • C
    $x = 4n + 1$, where $n$ is any positive integer
  • D
    $x = 2n + 1$, where $n$ is any positive integer
✓

Answer

Correct option: A.
$x = 4n$, where $n$ is any positive integer
a
(a) ${\left( {\frac{{1 + i}}{{1 - i}}} \right)^x} = 1,$

==> ${\left( {\frac{{1 + {i^2} + 2i}}{{1 + 1}}} \right)^x} = 1\,\, \Rightarrow \,{i^x} = 1\,$
$\therefore x = 4n,\,n \in {I^ + }$.

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