If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = a + ib, then what is 2 * 5 * 10….(1 + n^{2}) is equal to?

A)1+n^{2 }

B)x^{2}-y^{2}

c)x^{2}+y^{2}

d) none of these

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option C) is the correct

detailed solution ::

We have (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = x + iy …..(i)

(1 − i) (1 − 2i) (1 − 3i) ….. (1 − ni) = x − iy …..(ii)

Multiplying (i) and (ii),

we get 2 * 5 * 10 ….. (1 + n^{2}) = x^{2} + y^{2 }

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