Q. 105.0( 1 Vote )

# Mark the Correct alternative in the following:If (1 + i) (1 + 2i) (1 + 3i) … (1 + ni) = a + i b, then 2 . 5. 10 . 17 ……..(1 + n2) =A. a – ibB. a2 – b2C. a2 + b2D. None of these

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

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