Cunning Complex 1

Algebra Level 5

\[\large \left| { z }_{ 2 }{ z }_{ 3 }+{ 8z }_{ 3 }{ z }_{ 1 }+{ 27 }z_{ 1 }{ z }_{ 2 } \right| \]

If \(\left| { z }_{ 1 } \right| =1,\left| { z }_{ 2 } \right| =2,\left| { z }_{ 3 } \right| =3\) and \(\left| { z }_{ 1 }+{ 2z }_{ 2 }+{ 3z }_{ 3 } \right| =6\).Find the value of the expression above.

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