ComplexNumberBasic
Intermediate
If complex numbers $z_1, z_2, z_3$ satisfy
$$
\left\{
\begin{array}{l}
|z_1|=|z_2|=|z_3|=1\\
\\
\displaystyle\frac{z_1}{z_2}+\frac{z_2}{z_3}+\frac{z_3}{z_1}=1
\end{array}
\right.
$$
Compute $|az_1 +bz_2+cz_3|$ where $a, b, c$ are three given real numbers.
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