2022 VJC P1 Q5
Do not use a calculator in answering this question.
The complex number $z$ satisfies the equation
${{z}^{2}}-\left( 4+\mathbf{i} \right)z+2\left( \mathbf{i}-t \right)=0$,
where $t$ is a real number. It is given that one root is of the form $k-k\mathbf{i}$, where $k$ is real and positive. Find $t$ and $k$, and the other root of the equation.
[7]
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