= Solution
From the same multiplication, the <imaginary part> is
$$
\boxed{\Im Q=y_1x_2-x_1y_2=-(\mathbf v_1\times\mathbf v_2)_z.}
$$
Here the planar <vectors> are embedded in three dimensions with zero third coordinate. Its magnitude is the <area> of their <parallelogram>; its sign is positive when the oriented <angle> from $\mathbf v_2$ to $\mathbf v_1$ has positive <sine>. The reversed order matters: $\Im(z_1z_2^*)$ is the negative of the usual signed <area> for the order $(\mathbf v_1,\mathbf v_2)$.
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