Cunning Complex 1

Algebra Level 5

z2z3+8z3z1+27z1z2\large \left| { z }_{ 2 }{ z }_{ 3 }+{ 8z }_{ 3 }{ z }_{ 1 }+{ 27 }z_{ 1 }{ z }_{ 2 } \right|

If z1=1,z2=2,z3=3\left| { z }_{ 1 } \right| =1,\left| { z }_{ 2 } \right| =2,\left| { z }_{ 3 } \right| =3 and z1+2z2+3z3=6\left| { z }_{ 1 }+{ 2z }_{ 2 }+{ 3z }_{ 3 } \right| =6.Find the value of the expression above.

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