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

MCQ

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

A
$p = x,q = y$
B
$p = {x^2},\,\,q = {y^2}$
✓
$x = q,y = p$
D
None of these

✓

Answer

Correct option: C.

$x = q,y = p$

c
(c) $(x + iy)(p + iq) = ({x^2} + {y^2})i$
==> $(xp - yq) + i(xq + yp) = ({x^2} + {y^2})i$
==> $xp - yq = 0,xq + yp = {x^2} + {y^2}$
==> $\frac{x}{q} = \frac{y}{p}$and$xq + yp = {x^2} + {y^2}$
Let $\frac{x}{q} = \frac{y}{p} = \lambda $. then $x = \lambda q,y = \lambda p$
$xq + yp = {x^2} + {y^2}$

==> $\lambda = {\lambda ^2}$==> $\lambda = 1$

$x = q,y = p$.

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