QJEEM19Ma68f0: JEE Main 2019 Mathematics - Class 11 JEEM19Ma68f0 Solution: Let z 0 be a root of the quadratic equation, x 2 + x + 1 = 0,…

Question

Verified Solution • 2025–26 Session moderate

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 :

Accepted Answer

1 + x + x² = 0

x =

\frac{- 1 \pm \sqrt{1 - 4}}{2} = \frac{- 1 \pm i \sqrt{3}}{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}

(\frac{3}{3})

= tan^{$-$ 1} (1) =

\frac{π}{4}

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