Mark the Correct alternative in the following:
If (1 + i) (1 + 2i) (1 + 3i) …. (1 + n i) = a + i b, then 2 × 5 × 10 × … × (1 + n2) is equal to
Given that (1 + i) (1 + 2i) (1 + 3i) …. (1 + n i) = a + i b …(1)
We can also say that
(1 - i) (1 - 2i) (1 - 3i) …. (1 - n i) = a - i b …(2)
Multiply and divide the eq no. 2 with eq no. 1
((1)2 – (i)2)((1)2 – (2i)2)……((1)2 – (ni)2) = ((a)2 – (ib)2)
2 × 5 × 10 × …… × (1 + n2) = a2 + b2
1