Let z0 be a root of the quadratic equation, x2 + x + 1 = 0, If z = 3 + 6iz_0^81 - 3iz_0^93…

Question

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

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) = $${\pi  \over 4}$$

Solutions · 1