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  4. If ω is the cube root of unity, then (3+5 ω+3 ω2)2+(3+3 ω+5 ω2)2=

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Q. If $\omega$ is the cube root of unity, then $\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2=$

Complex Numbers and Quadratic Equations

Solution:

$\left(3+5 \omega+3 \omega^2\right)^2+\left(3+3 \omega+5 \omega^2\right)^2=(2 \omega)^2+\left(2 \omega^2\right)^2=4 \omega^2+4 \omega^4=-4$