AS FM Complex Numbers

You are given that |z-3| = 2|z-3+9i|

Show, using algebra with z = x + yi, that the locus of z is a circle and state the centre and radius of the circle.

I've been stuck on this question and mainly with how to treat the above equation. Any help would be greatly appreciated, thanks.

Reply 1

tonyiptony

11

Do you know what the modulus of a complex number, say x+yi, is? Recall...

Spoiler

Then rearrange terms.

Reply 2

BigJ123

10

Original post by aditi_idk

You are given that |z-3| = 2|z-3+9i|

Show, using algebra with z = x + yi, that the locus of z is a circle and state the centre and radius of the circle.

I've been stuck on this question and mainly with how to treat the above equation. Any help would be greatly appreciated, thanks.

Using our substitution of z=x+iy we'll get |(x+3) + iy| = 2|(x-3) + i(y+9)|

Then use the fact that tony sent to rearrange stuff and get the equation of a circle

(edited 10 months ago)

Reply 3

aditi_idk

OP

10

Original post by BigJ123

Using our substitution of z=x+iy we'll get |(x+3)-iy| = 2|(x-3) + i(y+9)|

Then use the fact that tony sent to rearrange stuff and get the equation of a circle