If   ,then

  • Option 1)

    x=2n,where  n  is any positive integer

  • Option 2)

    where  n  is any positive integer

  • Option 3)

    where  n  is any positive integer

  • Option 4)

    where  n  is any positive integer

 

Answers (2)

As we learnt in

Power of i in Complex Numbers -

i^{4n}=1,i^{4n+1}=i, i^{4n+2}=-1,i^{4n+3}=-i

- wherein

n\epsilon Integer

 

 \left(\frac{1+i}{1-i} \right )^{x}=1\ \; \Rightarrow\ \; \left[\frac{(1+i)(1+i)}{2} \right ]^{x}

=\left[\frac{(1+i)^{2}}{2} \right ]^{x}=\left[\frac{1-1+2i}{2} \right ]^{x}=(i)^{x}                                [For x = 4n]

i^{n}=1

Correct option is 4.

 


Option 1)

x=2n,where  n  is any positive integer

This is an incorrect option.

Option 2)

where  n  is any positive integer

This is an incorrect option.

Option 3)

where  n  is any positive integer

This is an incorrect option.

Option 4)

where  n  is any positive integer

This is the correct option.

N neha

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