If `(1+i)(1+2i)(1+3i)(1+n i)=(x+i y)` , Show that `2.5.10 ..... (1+n^2)=x^2+y^2dot`

Explanation

Given that,
` (1 + i) (1 + 2i) (1 + 3i) … (1 + ni) = x + iy ...(1)`


Taking conjugate, we get
` (1 – i) (1 – 2i) (1 – 3i) … (1 – ni) = x – iy ....(2)`


Multiplying Equations. (1) and (2), we get


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