The Real number line is in one dimension. If you want to map a complex number, you would have to add a second dimension to that number line- the Imaginary-axis.
The Imaginary-axis is always perpendicular to the Real-axis. Here is my question:
Would you still be able to use the complex plane if the imaginary-axis wasn't perpendicular to the Real-axis? In other words, is it still possible to prove theorems involving complex numbers (in a geometrical way) if the Imaginary-axis wasn't perpendicular to the Real-axis?
For example: Could you prove Euler's formula if the Imaginary-axis was tilted to a 45 degree angle?