- [Maximum mark: 7]
An electrical engineer models a circuit using the equation z² + 2tz + 8t = 0 where t is the time in seconds and 0 ≤ t ≤ 2.
(a) When t = 1, find the value of z which satisfies π/2 < arg z < π. 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 ≤ t ≤ 2 for which the power is maximized. [5]