Complex Numbers & Argand Diagrams | Edexcel A Level Further Maths: Core Pure Exam Questions 2017

3 marks

In an Argand diagram, the points $A$ and $B$ are represented by the complex numbers $- 3 + 2 i$ and $5 - 4 i$ respectively. The points $A$ and $B$ are the end points of a diameter of a circle $C$ .

(a)

Find the equation of

C,

giving your answer in the form

$| z - a | = b$ $a \in ℂ$ , $b \in ℝ$

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6 marks

The circle $D$ , with equation $| z - 2 - 3 i | = 2$ , intersects $C$ at the points representing the complex numbers $z_{1}$ and $z_{2}$

(b)

Find the complex numbers

z_{1}

and

z_{2}

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4 marks

$f (z) = z^{4} + a z^{3} + b z^{2} + c z + d$

where $a, b, c$ and $d$ are real constants.

Given that $- 1 + 2 i$ and $3 - i$ are two roots of the equation $f (z) = 0$

(a)

Show all the roots of

f (z) = 0

on a single Argand diagram.

How did you do?

5 marks

(b)

Find the values of

a, b, c

and

d .

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Complex Numbers & Argand Diagrams (Edexcel A Level Further Maths: Core Pure)

Exam Questions

1. Complex Numbers

1.1 Complex Numbers & Argand Diagrams

1.2 Exponential Form & de Moivre's Theorem

2. Matrices

2.1 Properties of Matrices

2.2 Transformations using Matrices

3. Further Algebra & Functions

3.1 Roots of Polynomials

3.2 Series

3.3 Maclaurin Series

4. Hyperbolic Functions

4.1 Hyperbolic Functions

5. Further Calculus

5.1 Volumes of Revolution

5.2 Methods in Calculus

6. Further Vectors

6.1 Vector Lines

6.2 Vector Planes

7. Polar Coordinates

7.1 Polar Coordinates

8. Differential Equations

8.1 First Order Differential Equations

8.2 Second Order Differential Equations

8.3 Simple Harmonic Motion

9. Proof

9.1 Proof by Induction