Question 16

16. [Maximum mark: 7]

An electrical engineer models a circuit using the equation:

$z^2 + 2tz + 8t = 0$

where $t$ is the time in seconds and $0 \le t \le 2$.

(a) When $t = 1$, find the value of $z$ which satisfies $\frac{\pi}{2} < \arg z < \pi$. Give your answer in the form $a + bi$. [2]

The power in the circuit is given by $|z|^2$.

(b) Find the value of $t$ in the interval $0 \le t \le 2$ for which the power is maximized. [5]