Complex Numbers And Quadratic Equations question 49
Question: If $ \frac{c+i}{c-i}=a+ib $ , where $ a,b,c $ are real, then $ a^{2}+b^{2}= $ [MP PET 1996]
Options:
A) 1
B) $ -1 $
C) $ c^{2} $
D) $ -c^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ \frac{c+i}{c-i}=a+ib $ …..(i) \ $ \frac{c+i}{c-i}=a+ib $ …..(ii) Multiplying (i) and (ii), we get $ \frac{c^{2}+1}{c^{2}+1}=a^{2}+b^{2} $
$ \Rightarrow a^{2}+b^{2}=1 $ .
BETA
