
Le discriminant de $3\i z^2 + 2z + \i$ est:
\[
\Delta = 2^2 - 4\times3\i\times\i = 4 - 12\i^2 = 4+12 = 16.
\]
Il y a donc deux solutions à $(E)$:
\[
z_1 = \dfrac{-2-\sqrt{16}}{2\times3\i} = -\dfrac{1}{\i} = -\dfrac{\i}{\i^2}=\i
\]
et
\[
z_2 = \dfrac{-2+\sqrt{16}}{2\times3\i} = \frac{1}{3\i} = -\dfrac{1}{3}\i.
\]
