If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib, then 2.5.10.....(1+ n 2 ) is equal to Options: A . &nbspa2-b2 B . &nbspa2+b2 C . &nbsp√a2+b2 D . &nbsp√a2−b2

Answer: Option B : B we have (1+i)(1+2i)(1+3i)......(1+ni) = a+ib .......(i) ⇒ (1+i)(1+2i)(1+3i)......(1+ni) = a-ib ........(ii) Multiplying (i) and (ii), we get 2.5.10.....(1+ n 2 ) = a 2 + b 2

If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib, then 2.5.10.....(1+n2) is equal to

Question

If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib, then 2.5.10.....(1+

n^{2}

) is equal to

Options:

A . a2-b2

B . a2+b2

C . √a2+b2

D . √a2−b2

Answer: Option B
:
B
we have
(1+i)(1+2i)(1+3i)......(1+ni) = a+ib .......(i)

\Rightarrow

(1+i)(1+2i)(1+3i)......(1+ni) = a-ib ........(ii)
Multiplying (i) and (ii), we get 2.5.10.....(1+

n^{2}

) =

a^{2}

b^{2}

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