Complex Numbers And Quadratic Equations question 131
Question: If $ (1+i)(1+2i)(1+3i)…..(1+ni)=a+ib $ , then 2.5.10…. $ (1+n^{2}) $ is equal to [Karnataka CET 2002; Kerala (Engg.) 2002]
Options:
A) $ a^{2}-b^{2} $
B) $ a^{2}+b^{2} $
C) $ \sqrt{a^{2}+b^{2}} $
D) $ \sqrt{a^{2}-b^{2}} $
Show Answer
Answer:
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} $
BETA
