Do functions exist so that they map from Complexes to

Step 1
There are lots of functions that map from Complexes to Reals.
The easiest such function is
\(Re(z)=a\)
for any
\(z=a+bi\)
This function just ignores the imaginary part of the complex number and outputs a real number. Here are a few examples
\(Re(1+2i)=1 \\Re(1–2i)=1 \\Re(pi+i)=pi \\Re(i)=0\)
Another natural such function is the magnitude function, which outputs the distance from zero for a given complex number. Using slightly non-standard function notation, magnitude can be shown like this
\(Mag(z)=(a^{2}+b^{2})(\frac{1}{2})\)
As a few examples,
\(Mag(3+4i)=5,\)
\(Mag(i)=Mag(-1)=1\)
(As a side note, you should recognize that the magnitude function is just the Pythagorean Theorem, solved for the hypotenuse)
Each of these functions is “onto” in the sense that for every “y” in the reals, there exists a complex “x” that maps to y; in other words,
f(x)=y
Neither of these functions is “one-to-one” because there are multiple complex numbers that map to the same real number; in other words Pf(a)=f(b) does not imply a=b.

Step 1
Given any two nonempty sets you can always find a function from one to the other. A function is just a type of relation where elements of the domain are related to only one element in the codomain.
An example of a function that takes complex numbers and maps them to real numbers would be the modulus of the complex number.
$$\begin{gathered} f:\mathbb{C}\to \mathbb{R} \\ f(z)=|z|=\sqrt{z\overline{z}} \end{gathered}$$
There are many others; including some boring ones like those that map everything to the same real value.