05 - The Argument(Angle) of a Complex Number

When we think of a complex number, we may plot it in rectangular form, (yes, there is another) as a point.

However, we can also imagine this complex number as a vector. A rectangle is just a parallelogram with right base angles. And so, we can find that this complex number is an arrow along the diagonal of this parallelogram.

And if we have a vector arrow, we can treat it like a pointed arrow, with a length and direction.

This is the , denoted , sometimes also as the angle, , which is also perfectly fine. It is found using trigonometry, where