Question

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

• A. $a^2$-$b^2$
• B. $a^2$+$b^2$
• C. $\sqrt{a^2+b^2}$
• D. $\sqrt{a^2-b^2}$

Answer 1

The correct option is B $a^2$+$b^2$

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+$n^2$) = $a^2$+$b^2$