Question

Prove that :-
(1+i^2+i^4+i^6.................+i^20)=1

Answer 1

1+(-1)+(-1)^2+(-1)^3.......+(-1)^10
=the answer will be zero I guess.

Answer 2

It's pretty simple
Divide all powers of i that are greater than or equal to 4 by 4 and put the remainder into the power
eg i^18
divide 18 by 4
remainder 2
rewrite it as i^2
so the new expression will be
(1+i^2+i^0+i^2+i^0+.......)
So if you extend
this upto 20 all terms except 1 will be cancelled
hence the answer 1
Hope it helps
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