Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz_0^{81} - 3iz_0^{93}, then arg z is equal to :

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Answer: A. {\pi \over 4} 1 + x + x2 = 0 x = {{ - 1 \pm \sqrt {1 - 4} } \over 2} = {{ - 1 \pm i\sqrt 3 } \over 2} z0 = w, w2 Now z = 3 + 6iz_0^{81} - 3iz_0^{93} z = 3 + 6iw81 - 3iw93 (w93 = w81 = 1) \Rightarrow z = 3 + 3i then arg(z) = tan-1\left( {{3 \over 3}} \right) = tan-1 (1) = {\pi \over 4}

Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz$$_0^{81}$$ $$-$$ 3iz$$_0^{93}$$, then arg z is equal to :

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