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simplify : (1+i/1-i)^(4n+1) n element of N pls answer it fast as i need the answer as soon as possible.

simplify : (1+i/1-i)^(4n+1)  n element of N pls answer it fast as i need the answer as soon as possible.

Grade:11

1 Answers

Vikas TU
14149 Points
7 years ago
(1+i/1-i)^(4n+1) can be ationalised.
First Rationalise it.

(1 + i)*(1+ i)/(1 – i^2) = > (1 – 1 + 2i)/(1 +1) 
                                 = > 2i/2 
                                = > i

Now,  i^(4n +1) = i^4n * i^1 = 1*I^1 = i (iota )
 

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