If $|z| = 2$. Then Locus of $z$ Representing The Complex no. $-1+5z,$ is

Question

$\underline{\bf{My\;\; Try::}}$ Let $z^{'} = -1+5z$, Where $z^{'} = x^{'}+iy^{'}$. So put $5z = z^{'}+1$ in $|z| = 2\Leftrightarrow |5z| = 10$

$|z^{'}-(-1+0\cdot i)| = 10$, means Locus of Conplex no. $z^{'}$ is a Circle with Center at $(-1,0)$

and Radious $ = 10$

Is it Right OR Not, If Not . The please explain me Righta answer.

Yes; multiplying by 5 is a dilation, and adding is a translation. — DBFdalwayse, Oct 10 '13 at 04:55

score 2 · Accepted Answer · answered Oct 10 '13 at 04:55

2

Well done! Your reasoning is spot on!

answered Oct 10 '13 at 04:55

Cameron Buie

1 Answers1