| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2007 |
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| Session | November |
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| Topic | Complex Numbers Argand & Loci |
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9 Write down, in any form, all the roots of the equation \(z ^ { 5 } - 1 = 0\).
Hence find all the roots of the equation
$$( w - 1 ) ^ { 4 } + ( w - 1 ) ^ { 3 } + ( w - 1 ) ^ { 2 } + w = 0$$
and deduce that none of them is real.
Find the arguments of the two roots which have the smaller modulus.