Standard +0.3 This is a straightforward Further Maths question with two standard parts: (i) solving a complex equation by multiplying through and equating real/imaginary parts, and (ii) using the modulus formula to find a parameter. Both require only routine algebraic manipulation with no novel insight, making it slightly easier than average even for Further Maths.
5. (i) Given that
$$\frac { 2 z + 3 } { z + 5 - 2 i } = 1 + i$$
find \(z\), giving your answer in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real constants.
(ii) Given that
$$w = ( 3 + \lambda \mathrm { i } ) ( 2 + \mathrm { i } )$$
where \(\lambda\) is a real constant, and that
$$| w | = 15$$
find the possible values of \(\lambda\).
5. (i) Given that
$$\frac { 2 z + 3 } { z + 5 - 2 i } = 1 + i$$
find $z$, giving your answer in the form $a + b \mathrm { i }$, where $a$ and $b$ are real constants.\\
(ii) Given that
$$w = ( 3 + \lambda \mathrm { i } ) ( 2 + \mathrm { i } )$$
where $\lambda$ is a real constant, and that
$$| w | = 15$$
find the possible values of $\lambda$.\\
\hfill \mbox{\textit{Edexcel F1 2018 Q5 [9]}}