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Idea not backed up by evidence is more of a hypothesis. A theory is a hypothesis proven true by evidence. It is something that applies to our current understanding of how something work and it can be modified or disproved in the future. In contrast, a law is a rule that applies to everything no...

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Let w=cis 2pi/9 i. Show that w^k is a solution of z^9-1=0 where k is an integer. ii. Prove that w + w^2 + w^3 + ... +w^8 = -1 iii. Hence show that cos(pi/9) cos(2pi/9) cost (4pi/9) = 1/8