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

Exam Questions

18 mins2 questions
1a
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3 marks

In an Argand diagram, the points A and B are represented by the complex numbers negative 3 plus 2 i and 5 minus 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 comma giving your answer in the form 

vertical line z minus a vertical line equals b      a element of straight complex numbersb element of straight real numbers

1b
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6 marks

The circle D, with equation vertical line z minus 2 minus 3 i vertical line equals 2, intersects C at the points representing the complex numbers z subscript 1 and z subscript 2

(b)
Find the complex numbers z subscript 1 and z subscript 2

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2a
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4 marks

space f left parenthesis z right parenthesis equals z to the power of 4 plus a z cubed plus b z squared plus c z plus d

where a comma space b comma space c and d are real constants.

Given that negative 1 plus 2 i and 3 minus i are two roots of the equation space f left parenthesis z right parenthesis equals 0

(a)
Show all the roots of space f left parenthesis z right parenthesis equals 0 on a single Argand diagram.
2b
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5 marks
(b)
Find the values of a comma space b comma space c and d.

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