Question 1420b

Complex Numbers

2020 Paper 1 Question 6 Variant

Question

The complex number

{z}

satisfies the equation

z^2(- 4 + 2 \mathrm{i}) - 8 z + t = 0,

where

{t}

is a real number. It is given that one root is of the form

{k + k \mathrm{i},}

where

{k}

is real and non-zero.

Find

{t}

and

{k,}

and the other root of the equation.

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