Absolute value and complex number

$\dfrac{|1512+ki|}{|2688+ki|} = \dfrac{3}{4}$

$\dfrac{\sqrt{1512^2+k^2}}{\sqrt{2688^2+k^2}} = \dfrac{3}{4}$

$\dfrac{1512^2+k^2}{2688^2+k^2} = \dfrac{9}{16}$

$16(1512^2+k^2)=9(2688^2+k^2)$

$7k^2=28449792$

$k^2=4064256$

$k=2016$ or $k=-2016$

$|k|$ = 2016