Physical significance of the complex numbers

Question

In case of the given statement below $\arg(z+i) =2π/3$ where $z$ is a complex numbers .

Here what is the physical way of seeing $z+i$, I mean does this represents a vector that joins $-i$ to $z$ or vice versa or something new as a whole ? Please help me to visualise this.

Answer 1

Any complex number can be viewed as a vector in the Argand plane. If you have a complex number $z = x + iy$, see it as a vector originating at (0, 0) with its head at $(x, y)$.

Let $\alpha = (a, b)$ be any given complex number ($i$ in your case). The complex number $z + \alpha$ is the vector $(x, y)$ originating at $\alpha = (a, b)$, with its head at $(x + a, y + b)$.

The argument of the complex number would be unchanged if its origin is translated.