$$x+iy=6+8i$$
$x=6+8i-iy$
$$x=6+8i-iy$$
$$x=-iy+\left(6+8i\right)$$
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$y=ix+\left(8-6i\right)$
$$iy=6+8i-x$$
$$\frac{iy}{i}=\frac{6+8i-x}{i}$$
$$y=\frac{6+8i-x}{i}$$
$$y=ix+\left(8-6i\right)$$
