Standard +0.8 This is a Further Maths FP2 question requiring manipulation of complex transformations. Students must substitute z = x (real), perform algebraic manipulation with complex fractions, separate real and imaginary parts, and eliminate the parameter to find the Cartesian equation. It requires solid technique with complex numbers but follows a standard method for this topic.
A transformation \(T\) from the \(z\)-plane to the \(w\)-plane is given by
$$w = \frac{z + 2i}{iz}$$
The transformation maps points on the real axis in the \(z\)-plane onto a line in the \(w\)-plane.
Find an equation of this line. [4]
A transformation $T$ from the $z$-plane to the $w$-plane is given by
$$w = \frac{z + 2i}{iz}$$
The transformation maps points on the real axis in the $z$-plane onto a line in the $w$-plane.
Find an equation of this line. [4]
\hfill \mbox{\textit{Edexcel FP2 Q1 [4]}}