The base $e^{5i\pi/2}$ is the <complex number> $i$. Principal exponentiation uses the principal logarithm of that base, so this is the same equation as in part iii:
$$
\boxed{z=\frac13+4k-\frac{2i\log2}{\pi},\qquad k\in\mathbb Z.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2018 / ia / Paper 1 / 1C / iv / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/ia/paper-1/1c/iv/solution