Standard +0.8 This Further Maths question requires expanding the product involving both z and its conjugate, separating real and imaginary parts, then solving the resulting simultaneous equations. It demands algebraic manipulation beyond standard complex number exercises and involves a non-standard form that requires insight to handle efficiently.
3. Given that \(z = x + \mathrm { i } y\), where \(x\) and \(y\) are real numbers, solve the equation
$$( z - 2 i ) \left( z ^ { * } - 2 i \right) = 21 - 12 i$$
where \(z ^ { * }\) is the complex conjugate of \(z\).
3. Given that $z = x + \mathrm { i } y$, where $x$ and $y$ are real numbers, solve the equation
$$( z - 2 i ) \left( z ^ { * } - 2 i \right) = 21 - 12 i$$
where $z ^ { * }$ is the complex conjugate of $z$.\\
\hfill \mbox{\textit{Edexcel F1 2015 Q3 [6]}}