The syllabus treats Euler’s formula as if it is a definition rather than an actual result. That means the only benefit of introducing it is simply notation.

But doing so does not explain why you can suddenly exponentiate a complex number and why this suddenly relates to the polar form of complex numbers.

You need to define e^x in the complex plane before you can exponentiate a complex number. There are different ways to do it.

One approach is to define e^x as a complex power series, which would lead to a question why it converges in the same way as the real counterpart.

Another approach is to define y=e^x as the solution to the complex differential equation dy/dx=y, ie. assume e^x can be differentiated in the same manner as a real function. This is not trivial for 4U students.

Yet another approach is to define e^x as a complex limit, which would lead to a question why the limit exists in the same way as the real counterpart.

Taking this formula as the definition is a cleaner approach for me because it defines real part and imaginary part of e^x separately, which makes the derivation of other results straight forward.