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# Complex Numbers

### 95-S1-Q4

de Moivre's theorem, binomial theorem, real and imaginary parts.

[STEP I 1995 Question 4 (Pure)]

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### 94-S3-Q6

Argand diagram, rotation, necessary and sufficient.

[STEP III 1994 Question 6 (Pure)]

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### 94-S1-Q6

Mobius transformation, real and imaginary part, conjugate, composition of functions.

[STEP I 1994 Question 6 (Pure)]

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### 93-S3-Q6

Argand diagram, circle, locus, Mobius transformation, position.

[STEP III 1993 Question 6 (Pure)]

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### 93-S1-Q5

Modulus, triangle inequality, roots of equation.

[STEP I 1993 Question 5 (Pure)]

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### 92-S2-Q10

Locus, argand diagram, real part, points on a circle.

[STEP II 1992 Question 10 (Pure)]

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### 91-S3-Q2

Argand diagram, triangles, rotation, deterinant of matrix, similar triangles, centroid, equilateral, geometry.

[STEP III 1991 Question 2 (Pure)]

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### 90-S3-Q1

de Moivre's theorem, trigonometry, roots of equation, tangent function.

[STEP III 1990 Question 1 (Pure)]

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### 90-S2-Q5

Geometry, circle, argand diagram, position.

[STEP II 1990 Question 5 (Pure)]

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### 89-S2-Q3

Ellipse, hyperbola, intersection, curve sketching.

[STEP II 1989 Question 3 (Pure)]

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## Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)