| Exam Board | CAIE |
|---|
| Module | FP1 (Further Pure Mathematics 1) |
|---|
| Year | 2010 |
|---|
| Session | June |
|---|
| Topic | Complex numbers 2 |
|---|
5 Use de Moivre's theorem to show that
$$\sin 5 \theta = 16 \sin ^ { 5 } \theta - 20 \sin ^ { 3 } \theta + 5 \sin \theta$$
Hence find all the roots of the equation
$$32 x ^ { 5 } - 40 x ^ { 3 } + 10 x + 1 = 0$$
in the form \(\sin ( q \pi )\), where \(q\) is a positive rational number.