Question 1411

Complex Numbers

2011 Paper 1 Question 10 Variant

Question

Do not use a graphic calculator in answering this question.

(i)

The roots of the equation

{z^2 = 8 \mathrm{i}}

are

{z_1}

and

{z_2.}

Find

{z_1}

and

{z_2}

in cartesian form

{x+\mathrm{i}y,}

showing your working.

[4]

(ii)

Hence, or otherwise, find in cartesian form the roots

{w_1}

and

{w_2}

of the equation

w^2 - 4 w + {\left( \textstyle 4 - 2 \mathrm{i} \right)}=0.

[3]

Answer

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