Question

Why the polar form(2.83,45) is written a rectangular complex number like this:
2.83*cos45 + j*(2.83*sin45)

I would like some explication please.

Thanks!

Answer 1

The "j" means there is a 90-degree phase
difference between the two terms and they cannot be added directly.

Another method of writing the polar form: 2.83[45o].

Answer 2

The i and j are unit vectors in the x any y directions.
This vector is of magnitude 2.83 and its direction is 45 degrees counterclockwise from the x axis so its components are
X direction: 2.83 * cos 45
Y direction: 2/83 * sin 45
so:
i * (2.83*cos45) + j*(2.83*sin45)