Complex Numbers And Quadratic Equations question 437
Question: If $ (x+iy)(p+iq)=(x^{2}+y^{2})i $ , then
Options:
A) $ p=x,q=y $
B) $ p=x^{2},q=y^{2} $
C) $ x=q,y=p $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ (x+iy)(p+iq)=(x^{2}+y^{2})i $
Þ $ (xp-yq)+i(xq+yp)=(x^{2}+y^{2})i $
Þ $ xp-yq=0,xq+yp=x^{2}+y^{2} $
Þ $ \frac{x}{q}=\frac{y}{p} $ and $ xq+yp=x^{2}+y^{2} $ Let $ \frac{x}{q}=\frac{y}{p}=\lambda $ . then $ x=\lambda q,y=\lambda p $ \ $ xq+yp=x^{2}+y^{2} $
Þ $ \lambda ={{\lambda }^{2}} $
Þ $ \lambda =1 $ \ $ x=q,y=p $ .
BETA
