Question 48
How many complex numbers $z$ are there that satisfy the following two conditions:
$$
|z| = 1, \quad \text{Re}(z^{100}) = \text{Im}(z^{200}) \quad ? \qquad (\text{Ilko Brnetić})
$$
$$
|z| = 1, \quad \text{Re}(z^{100}) = \text{Im}(z^{200}) \quad ? \qquad (\text{Ilko Brnetić})
$$