Given that 1+i1+22i×1+32i1+42i×....×1+(2n−1)2i1+(2n)2i=a+bic+di,s – InterviewSolution

1.	Given that 1+i1+22i×1+32i1+42i×....×1+(2n−1)2i1+(2n)2i=a+bic+di,showthat: 217×82257×....×(2n−1)4+1(2n)4+1=a2+b2c2+d2.
Answer» Given that $\frac{1 + i}{1 + 2^{2} i} \times \frac{1 + 3^{2} i}{1 + 4^{2} i} \times . . . . \times \frac{1 + (2 n - 1)^{2} i}{1 + (2 n)^{2} i} = \frac{a + b i}{c + d i}, s h o w t h a t :$ $\frac{2}{17} \times \frac{82}{257} \times . . . . \times \frac{(2 n - 1)^{4} + 1}{(2 n)^{4} + 1} = \frac{a^{2} + b^{2}}{c^{2} + d^{2}} .$

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