Stage: 5 Challenge Level: 
Evaluate without a calculator:
$(5\sqrt 2 + 7)^{{1\over 3}} - (5\sqrt 2 - 7)^{{1\over 3}}.$
Complex numbers. Long problems. Argand diagram. Complex roots of equations in conjugate pairs. Modulus arithmetic. Index notation/Indices. Powers & roots. Quadratic equations. Pythagoras' theorem. Surds.
Published February 1998.
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