If n be a positive integer,how to prove that (1+i)^n + (1-i)^n =2^(n+2)/2 cos nπ/4
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first write (1+I)^n in polar form as r(cos a + i sin a) where r is the modulus value .
and use Euler's theorem to write in the polar form as given in the picture.
then on adding them, i sin π/4 will get cancelled. then write √2 as 2^1/2 then you will get the answer
and use Euler's theorem to write in the polar form as given in the picture.
then on adding them, i sin π/4 will get cancelled. then write √2 as 2^1/2 then you will get the answer
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