4 Find the complex number \(z\) such that $$5 \mathrm { i } z + 3 z ^ { * } + 16 = 8 \mathrm { i }$$ Give your answer in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real.
[0pt] [6 marks] \(5 \quad\) A curve \(C\) has equation \(y = x ( x + 3 )\).

1. Find the gradient of the line passing through the point ( \(- 5,10\) ) and the point on \(C\) with \(x\)-coordinate \(- 5 + h\). Give your answer in its simplest form.
2. Show how the answer to part (a) can be used to find the gradient of the curve \(C\) at the point \(( - 5,10 )\). State the value of this gradient.
   [0pt] [2 marks] \(6 \quad\) A curve \(C\) has equation \(y = \frac { 1 } { x ( x + 2 ) }\).
3. Write down the equations of all the asymptotes of \(C\).
4. The curve \(C\) has exactly one stationary point. The \(x\)-coordinate of the stationary point is - 1 .
   1. Find the \(y\)-coordinate of the stationary point.
   2. Sketch the curve \(C\).
5. Solve the inequality $$\frac { 1 } { x ( x + 2 ) } \leqslant \frac { 1 } { 8 }$$