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Broad Topics > Advanced Algebra > Complex roots of equations in conjugate pairs

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Conjugate Tracker

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Make a conjecture about the curved track taken by the complex roots of a quadratic equation and use complex conjugates to prove your conjecture.

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Cube Roots

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Evaluate without a calculator: (5 sqrt2 + 7)^{1/3} - (5 sqrt2 - 7)^1/3}.