Question 1413a

Complex Numbers

2013 Paper 1 Question 4 Variant

Question

The complex number

{w}

is given by

{3 + \mathrm{i}.}

(a)

Find

{w^3}

in the form

{x+\mathrm{i}y,}

showing your working.

[2]

(b)

Given that

{w}

is ar root of the equation

az^3 - 122 z^2 + 290 z + b=0,

find the values of the real numbers

{a}

and

{b.}

[3]

(c)

Using these values of

{a}

and

{b,}

find all the roots of this equation in exact form.

[3]

Answer

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