de Moivre's theorem, trigonometric identities, arctan, induction.

[STEP II 2000 Question 4 (Pure)]

Triangle inequality, induction, roots of equation, geometry.

[STEP II 1998 Question 5 (Pure)]

Argand diagram, six-sided polygon.

[STEP I 1998 Question 5 (Pure)]

Roots of unity, points around a circle, coordinate geometry.

[STEP III 1997 Question 3 (Pure)]

Locus, subset, regions of Argand diagram.

[STEP II 1997 Question 5 (Pure)]

de Moivre's theorem, tangent identity, sum, cubic equation, roots of unity.

[STEP III 1996 Question 5 (Pure)]

Quartic equations, root of unity.

[STEP II 1996 Question 5 (Pure)]

Quadratic equations, rational numbers.

[STEP I 1996 Question 5 (Pure)]

Argand diagram, inverse function.

[STEP III 1995 Question 6 (Pure)]

Roots of quadratics, roots of unity.

[STEP II 1995 Question 6 (Pure)]