Complex Numbers

de Moivre's theorem, trigonometry, roots of polynomial equation.

[STEP I 1989 Question 8 (Pure)]

Argand diagram, locus.

[STEP II 1988 Question 4 (Pure)]

Argand diagram, perpendicular, geometry, real part, convex hexagon, distance.

[STEP I 1988 Question 6 (Pure)]

Inequality, binomial expansion, trigonometric identity, arctan function.

[STEP II 1987 Question 3 (Pure)]

Argand diagram, geometry, necessary and sufficient, if and only if, vertices of equilateral triangle.

[STEP II 1987 Question 4 (Pure)]

Triangle inequality, solution of complex polynomial equation.

[STEP III Specimen Question 3 (Pure)]

de Moivre's theorem, system and simultaneous equations, trigonometry.

[STEP II Specimen Question 3 (Pure)]

Modulus and argument, complex exponential, de Moivre's theorem, sum of complex series.

[STEP I Specimen Question 7 (Pure)]