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
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 }