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 + n^{2}) =

A. a – ib

B. a^{2} – b^{2}

C. a^{2} + b^{2}

D. None of these

Answer :

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 + n^{2}) = a^{2} + b^{2}

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