Show that if $|z|=2$, $\text{Im}(1-\bar{z}+z^2)\le 7$.
By the triangle inequality:
$$|1 + (-\bar{z}) + z^2 | ≤ |1| + |-\bar{z}| + |z^2| ≤ 1+2+2^2 = 7$$
(think about what happens to $z = 2e^{i \theta}$).
Show that if $|z|=2$, $\text{Im}(1-\bar{z}+z^2)\le 7$.
By the triangle inequality:
$$|1 + (-\bar{z}) + z^2 | ≤ |1| + |-\bar{z}| + |z^2| ≤ 1+2+2^2 = 7$$
(think about what happens to $z = 2e^{i \theta}$).