P4 Complex numbers

guys i got a tiny problem in the january 2004 paper in 2b (iii) where it asks u u write down an equation for L2 in which z occurs only once

Context
the locus L2 consists of the points representing complex numbers z for which |z-9j| = 2|z-12|
ps before that question i was asked to show that L2 is a circle. i did the eqaution i obtained was (x-16)²+(y+3)² = 100

pls help before my exam on tues
thanx

Reply 1

yazan_l

well L2 is the circle with centre 16-3i, and radius (modulus) 10

Edit: well actually i dont know if that is what you want!

Reply 2

the sometimes sunshine child

Hey I'm doing the same question, but I got stuck at part (i) :confused:

How do you know the third asymptote of y= (x-9)/(x+7)(x-5) is y=0

Somehow, I've managed to get y=1/(x+2)

Reply 3

krish87

OF COURSE U ARE CORRECT YASAN !!! how did u figure that out pls explain

ps teh answe is |z-(16-3j)|=10 . is that what u mean?

Reply 4

the sometimes sunshine child

Actually, what am i talking about, I doing the same paper, but got stuck on question one.

How do you know the third asymptote of y= (x-9)/(x+7)(x-5) is y=0

I presume chubby has done this, please could you help?

Reply 5

Gaz031

chubby

OF COURSE U ARE CORRECT YASAN !!! how did u figure that out pls explain

ps teh answe is |z-(16-3j)|=10 . is that what u mean?

Remember that a circle centre (a,b) radius r has equation (x-a)^2+(y-b)^2=r^2 and the equivelant equation for a complex number x+iy is modulus[z-(a+ib)]=r

Reply 6

krish87

ok natsy

basically what u got to do is divide the whole thing by the highest co-efficeint of x from the denominater to every term to amd bottom (in this case x^2) so the equation u obtain.............. substitue any high number say 10000000 as x. overall the answer will tend towards 0. so y=0 is teh asmptote. hope u get what i mean.

Reply 7

the sometimes sunshine child

Thanks- I'm just panicking now. I forgot to substitute the large x.

What can i say, except too many maths papers-ironic i know. Exam on Tuesday...

Reply 8

krish87

ps did u get your graph correctly or was it wrong?

mine was wrong but did not liek the question either but liked 2, 3, 4!!! so u know decided to drop q1! but still.... i hope on tues i dont get a graph q liek that. lol

Reply 9

the sometimes sunshine child

Yep, apart from the initial (albeit rather large) setback, my graph is now correct.

I'm halfway through the second question, but finding hard. But I'm doing FP1, so maybe that's why (hopefully)...