| Exam Board | Edexcel |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Topic | Complex Numbers Arithmetic |
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| Type | Factored form to roots |
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11. (a) Using that 3 is the real root of the cubic equation \(x ^ { 3 } - 27 = 0\), show that the complex roots of the cubic satisfy the quadratic equation \(x ^ { 2 } + 3 x + 9 = 0\).
(b) Hence, or otherwise, find the three cube roots of 27, giving your answers in the form \(a + \mathrm { i } b\), where \(a , b \in \mathbb { R }\).
(c) Show these roots on an Argand diagram.