Complex Numbers (CIE A Level Maths: Pure 3)

Exam Questions

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2 marks

$z_{1} = 3 + i$ and $z_{2} = - 5 + 2 i$

(i)

Work out

z_{1} + z_{2}

and

z_{1} - z_{2} .

(ii)

Use your answers to part (i) to write down

Re (z_{1} + z_{2})

and

Im (z_{1} - z_{2}) .

How did you do?

2 marks

By first writing $z_{1} \times z_{2} = (3 + i) (- 5 + 2 i)$ , and then expanding brackets and using the fact that $i^{2} = - 1$ , show that

$z_{1} \times z_{2} = - 17 + i$

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Complex Numbers (CIE A Level Maths: Pure 3)

Exam Questions

1. Algebra & Functions

1.1 Modulus Functions

1.2 Polynomials

1.3 Partial Fractions

1.4 Further Modelling with Functions

1.5 General Binomial Expansion

2. Logs & Exponentials

2.1 Logarithmic & Exponential Functions

2.2 Laws of Logarithms

2.3 Modelling with Logs & Exponentials

3. Trigonometry

3.1 Reciprocal Trigonometric Functions

3.2 Compound & Double Angle Formulae

3.3 Further Trigonometric Equations

3.4 Trigonometric Proof

4. Differentiation

4.1 Further Differentiation

4.2 Implicit Differentiation

4.3 Differentiation of Parametric Equations

5. Integration

5.1 Further Integration

5.2 Differential Equations

6. Numerical Methods

6.1 Numerical Solutions of Equations

7. Vectors

7.1 Vectors in 2 Dimensions

7.2 Vectors in 3 Dimensions

7.3 Further Vectors

8. Complex Numbers

8.1 Complex Numbers

8.2 Argand Diagrams

8.3 Further Complex Numbers