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FP2 Edexcel Complex Plane Transformation Need help!

Question: https://gyazo.com/c7db45f12d47aca8a58575fc7eaa22da
Book's solution: https://gyazo.com/5f4827baf8d45e35aede1419089a5a43
https://gyazo.com/9a3ea9ab090078f825204a2e6a0ed0da
My question: For the solution of QB, with

Unparseable latex formula:

\displaystyle\begin{equation*}\ {x} = 4\end{equation*}

why is

Unparseable latex formula:

\displaystyle\begin{equation*} \frac{u}{u^2+v^2} = 2 \end{equation*}

Shouldn't it be

Unparseable latex formula:

\displaystyle\begin{equation*} \frac{u}{u^2+v^2} = 4? \end{equation*}

Thanks in advance.

Reply 1

Zacken

Original post by Nerrad

...

At a glance, I seemingly agree with you, although it seems like a fairly bizarre error to make.

Reply 2

Nerrad

Original post by Zacken

At a glance, I seemingly agree with you, although it seems like a fairly bizarre error to make.

And yet their working out continues, and seems to have a final (assuming it's correct) answer?

Reply 3

Zacken

Original post by Nerrad

And yet their working out continues, and seems to have a final (assuming it's correct) answer?

Yeah, it's defo wrong - just had a proper look.

Should be this:

\frac{u}{u^2 + v^2} = 4 \Rightarrow u = 4u^2 + 4v^2 \Rightarrow u^2 + v^2 - \frac{u}{4} =0

\left(u - \frac{1}{8}\right)^2 - \frac{1}{64} + v^2 = 0 \Rightarrow \left(u - \frac{1}{8}\right)^2 + v^2 = \left(\frac{1}{8}\right)^2

.

Circle centre

\left(\frac{1}{8}, 0\right)

and radius

\frac{1}{8}

(edited 8 years ago)

Reply 4

B_9710

Original post by Zacken

Yeah, it's defo wrong - just had a proper look.

Should be this:

\frac{u}{u^2 + v^2} = 4 \Rightarrow u = 4u^2 + 4v^2 \Rightarrow u^2 + v^2 - \frac{u}{4} =0

\left(u - \frac{1}{8}\right)^2 - \frac{1}{16} + v^2 = 0 \Rightarrow \left(u - \frac{1}{8}\right)^2 + v^2 = \left(\frac{1}{4}\right)^2

.

Circle centre

\left(\frac{1}{4}, 0\right)

and radius

\frac{1}{4}

Radius =1/8 :biggrin:

Reply 5

Zacken

Original post by B_9710

Radius =1/8 :biggrin:

Oh gosh, thanks!! :lol:

Reply 6

B_9710

Original post by Zacken

Oh gosh, thanks!! :lol:

Reply 7

Nerrad

Thanks guys

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