Question

Sketching complexes

Answer 1

http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w10_qp_33.pdf
3(ii)

Answer 2

Question 3(ii)

Answer 3

From i)
I've got
w=2+i

\[w^2=(2+i)^2 \\ \\ w^2=4+4i+4i^2 \\ \\ w^2=3+4i\]

Answer 4

Modulus of \(w^2\) is \(|w^2|=\sqrt{9+16}=5\)

Answer 5

How do I sketch
\[|z-w^2| \leq |w^2|\]

Answer 6

\[w^2=(2+i)^2=4+4i+i^2=4+4i-1=3+4i\]

Answer 7

Is it correct?

Answer 8

i think so, but im not sure about where to shade

Answer 9

hmm, the marking scheme is here, maybe it'll help
http://papers.xtremepapers.com/CIE/Cambridge%20International%20A%20and%20AS%20Level/Mathematics%20%289709%29/9709_w10_ms_33.pdf

Answer 10

oh its a circle

Answer 11

we can see from \(|z-w^2|\leq|w^2|\),
that if \(z\) is in the same direction as \(w\) ;

\(z\) must be \(0\leq z\leq2w^2\)