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  4. If (x+iy)(p+iq)=(x2+y2) i , then

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

Complex Numbers and Quadratic Equations

Solution:

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