Yep!

4i can be re-written as 0+4i, like you said.

That said 3 (which can be written as 3+0i) is *also* a complex number!

Complex numbers are a superset of the real numbers, meaning that all real numbers are complex numbers. This is similar to how all integers are rational numbers, or how all rational numbers are real numbers. Whether you see 3 as a real number or a complex number is entirely context-dependent, and either option is correct.