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

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Medium

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)

Topic Questions