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  4. Let z0 be a root of the quadratic equation, x2 + x + 1 = 0. If z = 3 + 6iz081 -3iz093 , then arg z is equal to :

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Q. Let $z_0$ be a root of the quadratic equation, $x^2 + x + 1 = 0$. If $z = 3 + 6iz_0^{81} -3iz_0^{93}$ , then arg $z$ is equal to :

JEE MainJEE Main 2019Complex Numbers and Quadratic Equations

Solution:

$z_0 = \omega$ or $\omega^2$ (where $\omega$ is a non-real cube root of unity)
$z = 3 + 6i(\omega)^{81} - 3i(\omega)^{93}$
z = 3 + 3i
$\Rightarrow \; \arg \; z = \frac{\pi}{4}$