If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = x + iy, then what is 2 * 5 * 10….(1 + n2) is equal to?

Question

If (1 + i) (1 + 2i) (1 + 3i) ….. (1 + ni) = a + ib, then what is 2 * 5 * 10….(1 + n²) is equal to?

A)1+n² 

B)x²-y²

c)x²+y²

d) none of these 

Answer 1

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 + n²) = x² + y²