Q.Represent $z=2+3i$ and its conjugate $\bar z$ on the Argand plane, and state the geometric relationship between the two points.

The Argand plane (or complex plane) is the geometric picture of the complex numbers: a complex number $z=x+iy$ is represented as the unique point $P(x,y)$ in a plane with a horizontal real axis (carrying $\mathrm{Re}(z)$) and a vertical imaginary axis (carrying $\mathrm{Im}(z)$). Every real number sits on the real axis, and every purely imaginary number sits on the imaginary axis, so the familiar real number line is just one axis inside this larger picture. The conjugate $\bar z=x-iy$ of $z$ is the reflection of $P$ in the real axis, and $-z$ is the reflection of $P$ through the origin. This one-to- …