What's the name of the form $ai+b$ of a complex number?

Question

Example: the number $0.5$ can be written as a fraction $\frac {1}{2}$.

Is there an official name for writing a number in the form of $ai + b$?

Complex numbers could also be written in this form $z = a\ e^{i \theta}$. What is that form called?

Answer 1

I would usually call $a+bi$ the rectangular form, and $re^{i\theta}$ the polar form. -- René B. Christensen

Rectangular form is also known as Cartesian form. –- abel

Answer 2

Standard Form. Source: http://www.regentsprep.org/regents/math/algtrig/ato6/imagineles.htm

(Plus, I think that's what my school calls it.)