Complex Numbers And Quadratic Equations question 641
Question: If $ (a+ib)(c+id)(e+if)(g+ih)=A+iB, $ then $ (a^{2}+b^{2})(c^{2}+d^{2})(e^{2}+f^{2})(g^{2}+h^{2})= $
Options:
A) $ A^{2}+B^{2} $
B) $ A^{2}-B^{2} $
C) $ A^{2} $
D) $ B^{2} $
Show Answer
Answer:
Correct Answer: A
Solution:
$ (a+ib)(c+id)(e+if)(g+ih)=A+iB $ …(i)
$ \Rightarrow (a-ib)(c-id)(e-if)(g-ih)=A-iB $ …(ii) Multiplying (i) and (ii), we get $ (a^{2}+b^{2})(c^{2}+d^{2})(e^{2}+f^{2})(g^{2}+h^{2})=A^{2}+B^{2} $
BETA
