A) \[{{a}^{2}}-{{b}^{2}}\]
B) \[{{a}^{2}}+{{b}^{2}}\]
C) \[\sqrt{{{a}^{2}}+{{b}^{2}}}\]
D) \[\sqrt{{{a}^{2}}-{{b}^{2}}}\]
Correct Answer: B
Solution :
We have \[(1+i)(1+2i)(1+3i).....(1+ni)=a+ib\] .....(i) Þ \[(1-i)(1-2i)(1-3i).....(1-ni)=a-ib\] .....(ii) Multiplying (i) and (ii), we get \[2.5.....(1+{{n}^{2}})={{a}^{2}}+{{b}^{2}}\]
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