book Maths Puzzle Numerical Ability

find the value of -
(i+3^.5)^100 + (i-3^.5))^100 + 2)^100

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book Other Question

What is the sum of (2n+1)squared using 0<n<infinity? Let Pn[X] be the vector space of all polynomials of degree <=n, prove that the set (1,x,x(x-1),x(x-1)(x-2),...,x(x-1)(x-2)***(x-n+1)) is a basis for this vector space.

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