Find the roots of the equation \(m ^ { 2 } + 2 m + 2 = 0\) in the form \(a + i b\).
(2 marks)
Find the general solution of the differential equation
$$\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} x ^ { 2 } } + 2 \frac { \mathrm {~d} y } { \mathrm {~d} x } + 2 y = 4 x$$
Hence express \(y\) in terms of \(x\), given that \(y = 1\) and \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 2\) when \(x = 0\).