Q.If $z=3+5i$ then represent $z,\ \bar z,\ -z,\ -\bar z$ in Argand's diagram.

The Argand diagram (or complex plane) represents each complex number $z=x+iy$ as the single point $P(x,y)$ in an ordinary two-dimensional plane, using the one-to-one correspondence between complex numbers and plane points first proposed by Jean Robert Argand. The horizontal axis carries the real part $x=\mathrm{Re}(z)$ and is called the real axis; the vertical axis carries the imaginary part $y=\mathrm{Im}(z)$ and is called the imaginary axis. This turns every algebraic fact about complex numbers into a geometric one: addition of complex numbers corresponds to vector addition of the corresponding points, the conjugate $\bar z$ is the reflection of $z$ across the real axis, and $-z$ is the point diametrically opposite $z$ through the origin. This geometric picture is also what makes the modulus and argument meaningful (the modulus is …