Question

If $(x+iy)(p+iq)=(x^2+y^2)i$ , then

• A. $p=x^2,q=y^2$
• B. $x=q$ , $y=p$
• C. $p=x$, $q=y$
• D. $p=-x$, $q=y$

Answer 1

Answer: (B)

Since $x^2+y^2=\left(x+iy\right)\left(x-iy\right)$
$\therefore \left(p+iq\right)=\left(\frac{x^2+y^2}{x+iy}\right)i$
$=\left(x-iy\right)i$
$=y+ix$
$\therefore p=y$ ,
$q=x$