Question

Nobody can help me. This question is here like for 1 hour:
Locus of points z:
|z-2|-|z+2|>3

Answer 1

x< -2

Answer 2

how you got that?

Answer 3

wait,

Answer 4

it not 2, it's x<-3/2

Answer 5

but explain how you got it

Answer 6

hit and trial ,,, have to wait for theory

Answer 7

i don't have correct answer. And not making any test. Just studying...

Answer 8

|z-2|-|z+2| > |z|+|2|-|z+2| >|z|+|2|-|z|-|2| > 3 => 2|z| > 3
=> z > 3/2 or -z < 3/2
case 1 doesn't work so case 2 ... hahah ... lol
good night 3 am here

Answer 9

I get something like this:
\[28x ^{2} -14x +81>36y ^{2}\]

Answer 10

have to sleep ... can we discuss tomorrow?

Answer 11

|z-2|>|z|+|2|?
kk, goodnight

Answer 12

oops sorry mistake here
=> z > 3/2 (for positive z) or z < -3/2 (for negative z)
good night

Answer 13

|z-2|>|z|-|2|

Answer 14

|z-2|>|z|+|2| wrong

Answer 15

z is complex number

Answer 16

Oo ,,, sorry .. wrong assumption. let's discuss tomorrow

Answer 17

kk, thx

Answer 18

|z-2|-|z+2|>3
|z-2|>3+|z+2|
|x+yi-2|>3+|(x+yi)+2|
|(x-2)^2+y^2|>3+|(x+2)^2+y^2|
x^2-4x+4+y^2>3+(x^2+4x+4)+y^2
-4x+4>4x+7
-8x>3
x<3/8

Answer 19

|(x-2)^2+y^2|>3+|(x+2)^2+y^2|
??
should't be square root?

Answer 20

yeah sqrt is missing ..

Answer 21

let wolf do the calc
http://www.wolframalpha.com/input/?i=%28%28x-2%29%5E2%2By%5E2%29%5E%281%2F2%29%3E+3%2B%28%28x%2B2%29%5E2%2By%5E2%29%5E%281%2F2%29

Answer 22

I can come to this expression:
\[14x(x-1/2)>9(y^{2}-9/4)\]
anybody recognize what's that??

Answer 23

whoops forgot the square root
\[\sqrt{(x-2)^2+y^2}>\sqrt{(x+2)^2+y^2}+3\]

Answer 24

but then yout result is wrong

Answer 25

you just need to sqrt both sides
then the \[x<-\frac{3}{2} \]

Answer 26

\[(x-2)^{2}+y ^{2}>(x+2)^{2}+y ^{2} +6\sqrt{(x+2)^{2}+y ^{2}} +9\]

Answer 27

can you show me how you got that? @.Sam.

Answer 28

which one?

Answer 29

x<-3/2

Answer 30

the one that was before the last ?