7 The equation \(2 x ^ { 3 } + x ^ { 2 } + 25 = 0\) has one real root and two complex roots.
- Verify that \(1 + 2 \mathrm { i }\) is one of the complex roots.
- Write down the other complex root of the equation.
- Sketch an Argand diagram showing the point representing the complex number \(1 + 2 \mathrm { i }\). Show on the same diagram the set of points representing the complex numbers \(z\) which satisfy
$$| z | = | z - 1 - 2 \mathrm { i } |$$