If \(|z_1| = 2, |z_2| = 3, |z_3| = 4\) and \(|2z_1 + 3z_2 + 4z_3| = 4\), then absolute value of \(8z_2z_3 + 27z_3z_1 + 64z_1z_2\) equals
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When you see expressions like \(k_1 z_2 z_3 + k_2 z_3 z_1 + k_3 z_1 z_2\), always try to factor out \(z_1 z_2 z_3\) and use the identity \(1/z = \bar{z}/|z|^2\). This often simplifies the problem to a known modulus given in the question.