Transformations from the z-plane to the w-planeEdexcel A-Level Further Maths: Mind map

Method

$w=az+b$

$w=z^2$

z-plane to w-plane

transformations of loci

w=az+b

w=z^2

w=\frac1z

Möbius

$w=\frac1z$

Möbius

Exam tips

Exam questions on Transformations from the z-plane to the w-plane

The transformation $T$ from the $z$ -plane to the $w$ -plane is given by $w=3z+2i$ , where $z=x+iy$ and $w=u+iv$ .
Find the Cartesian equation of the image of the line $y=x$ in the $z$ -plane.2 marks
The transformation $T$ from the $z$ -plane to the $w$ -plane is given by $w=z^2$ , where $z=x+iy$ and $w=u+iv$ .
Find the image of the line $y=x$ in the $w$ -plane.2 marks
The transformation $T$ from the $z$ -plane to the $w$ -plane is given by $w=\frac{1}{z}$ , where $z=x+iy$ and $w=u+iv$ .
Show that the image of the line $x=1$ in the $z$ -plane is a circle in the $w$ -plane, and find its centre and radius.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).