Complex numbers why

Where were complex numbers first used?
Complex numbers were introduced by the Italian famous gambler and mathematician Gerolamo Cardano (1501--1576) in 1545 while he found the explicit formula for all three roots of a cube equation..
Why do we have complex numbers?
The system of complex numbers is essential to the field because it is a convenient language for expressing wave functions without breaking the rules.
Furthermore, a direct application of Quantum Mechanics is that it accelerated the expansion of Chemistry..
Why do we need imaginary numbers?
Why do we have imaginary numbers anyway? The answer is simple.
The imaginary unit ‍ allows us to find solutions to many equations that do not have real number solutions..
Complex numbers are a nice compact way of representing waves because of Euler's formula : This is used in a variety of domains, not just quantum mechanics.
It gives you a natural way to compress the two dimensions of the wave (e.g. “phase” and “amplitude”) into a single value.

Where were complex numbers first used?