If z_1, z_2, z_3 are the roots of the equatio | vedclass

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(D) For a cubic equation of the form $az^3 + bz^2 + cz + d = 0$, the sum of the roots $z_1 + z_2 + z_3$ is given by $-\frac{b}{a}$.Here, the given equ

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$4$

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(D) For a cubic equation of the form $az^3 + bz^2 + cz + d = 0$, the sum of the roots $z_1 + z_2 + z_3$ is given by $-\frac{b}{a}$.Here, the given equation is $z^3 - z^2(4 + 3i) + z(3 + 8i) - 5i = 0$.Comparing this with the standard form, we have $a = 1$ and $b = -(4 + 3i)$.Therefore, the sum of the roots is $z_1 + z_2 + z_3 = -\frac{-(4 + 3i)}{1} = 4 + 3i$.We are asked to find $Re(z_1) + Re(z_2) + Re(z_3)$, which is equal to $Re(z_1 + z_2 + z_3)$.Since $z_1 + z_2 + z_3 = 4 + 3i$, the real part is $Re(4 + 3i) = 4$.Thus, $Re(z_1) + Re(z_2) + Re(z_3) = 4$.

If $z_1, z_2, z_3$ are the roots of the equation $z^3 - z^2(4 + 3i) + z(3 + 8i) - 5i = 0$, then $Re(z_1) + Re(z_2) + Re(z_3)$ is -

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