I am trying to solve a problem using Euler's relations, I am not sure where to start with it, here is the question :
Using Euler's relations, simplify $z = e^{2+i\pi/2}$
If someone could explain to me how to do this, including the methodology from start to finish I would be very grateful as I am struggling with this.
Note that
$$\begin{align} e^{2+i\pi/2}&=e^2e^{i\pi/2}\\\\ &=e^2\left(\cos(\pi/2)+i\sin(\pi/2)\right)\\\\ &=ie^2 \end{align}$$
$$ e^{2+i\pi/2} = e^2 e^{i\pi/2} = \cdots $$ If by "Euler's relations" you mean $e^{i\theta} = \cos\theta+i\sin\theta,$ then that applies to $e^{i\pi/2}.$
$$e^{2+\frac{\pi}{2}i} = e^2 \cdot e^\frac{\pi}{2}i = e^2 \left( \cos \frac{\pi}{2} + i \sin \frac{\pi}{2}\right) = e^2 ( 0 + i\cdot 1) = ie^2$$