Mathematics - Complex Number Question with Solution | TestHub

$\left|8z_2{z}_3+27z_3{z}_1+64z_1{z}_2\right|=\left|z_1\right|\left|z_2\right|\left|z_3\right|$ $\left|\frac{8}{z_1}+\frac{27}{z_2}+\frac{64}{z_3}\right|$ $=(2)(3)(4)\left|\frac{8{\bar{z}}_1}{{|z_1|}^2}+\frac{27{\bar{z}}_2}{{|z_2|}^2}+\frac{64{\bar{z}}_3}{{|z_3|}^2}\right|$ $=24\left|2{\bar{z}}_1+3{\bar{z}}_2+4{\bar{z}}_3\right|$ $=24\left|\overline{2z_1+3z_2+4z_3}\right|$ $=24\left|2z_1+3z_2+4z_3\right|=(24)(4)=96$