# Complex Egyptian Fractions

$\dfrac{5}{4-3i} = \dfrac{1}{v} + \dfrac{1}{w} + \dfrac{1}{z}$

Let $v,w,z$ be the Gaussian integers, satisfying the equations above, where $1< |v| < |w| < |z|$ and $v+w+z$ is real.

What is the least possible value of $|v|^2 + |w|^2 + |z|^2$?

Note: $i^2 = -1$, and $|z|$ is the absolute value of $z$.

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