Solution
= Solution
Write $z=x+iy$, with real $x,y$. Its <complex conjugate> is $z^*=x-iy$, so equating real and imaginary parts gives $4x=1$, $2y=1$. Thus the <complex plane> locus is the single point
$$
\boxed{z=\frac14+\frac i2.}
$$
= Solution
Write $z=x+iy$, with real $x,y$. Its <complex conjugate> is $z^*=x-iy$, so equating real and imaginary parts gives $4x=1$, $2y=1$. Thus the <complex plane> locus is the single point
$$
\boxed{z=\frac14+\frac i2.}
$$