Standard +0.3 This is a straightforward Further Maths question testing basic complex number manipulation: (i) requires multiplying by conjugate and simplifying - a routine algebraic exercise, and (ii) requires expanding, using tan(arg z) = Im/Re, and solving a linear equation. Both parts are standard textbook exercises with no novel insight required, though slightly above average difficulty due to being Further Maths content.
7. (i) Given that
$$\frac { 2 w - 3 } { 10 } = \frac { 4 + 7 i } { 4 - 3 i }$$
find \(w\), giving your answer in the form \(a + b \mathrm { i }\), where \(a\) and \(b\) are real constants. You must show your working.
(ii) Given that
$$z = ( 2 + \lambda i ) ( 5 + i )$$
where \(\lambda\) is a real constant, and that
$$\arg z = \frac { \pi } { 4 }$$
find the value of \(\lambda\).
□
7. (i) Given that
$$\frac { 2 w - 3 } { 10 } = \frac { 4 + 7 i } { 4 - 3 i }$$
find $w$, giving your answer in the form $a + b \mathrm { i }$, where $a$ and $b$ are real constants. You must show your working.\\
(ii) Given that
$$z = ( 2 + \lambda i ) ( 5 + i )$$
where $\lambda$ is a real constant, and that
$$\arg z = \frac { \pi } { 4 }$$
find the value of $\lambda$.\\
□\\
\hfill \mbox{\textit{Edexcel F1 2014 Q7 [8]}}