Complex # Locus Qs. (I Need Serious Help) (1 Viewer)

[Sparcod]

Hey Everyone.

1. |z- (-2+4i) | = 2 |z-(4+i)| This is a circle. What's its radius and centre? How do you work it out?

2. z = x+iy

2 |z| = z +Z + 4

prove that this is a parabola. ( big Z should be a conjugate, you know -with the stroke above it)

All help is much appreciated.

 

[shsshs]

1.
let z = x + iy and u know that lzl = sqrt(x^2 + y2)

so you get

sqrt[ (x + 4)^2 + (y - 4)^2 ] = 2sqrt[ (x -4)^2 + (y - 1)^2]

then u just square both sides and simplify


2. same thing lzl = sqrt ( x^2 + y^2)

so 2sqrt(x^2 + y^2) = 2x + 4

then you square both sides and simplify and you get

4y^2 = 16(x + 1)
which is a sideways parabola

 

[shimmerz_777]

heres a tip, if you ahve a mod of z like lz - (a + bi)l than its point on the argand diagram will be a and bi. like you dont need to go finding the center straight away and stuff, and if its a simple question you can just plot it without having to do any work

 

[bboyelement]

how would you plot |z - 2| = |Z - 2| note Z is conjugate z

 

[Sober]

how would you plot |z - 2| = |Z - 2| note Z is conjugate z

That should hold true for all z, so to plot it you would end up with a shaded piece of paper.

 

[Riviet]

how would you plot |z - 2| = |Z - 2| note Z is conjugate z

Wouldn't that be all points on the Argand diagram? I can't think of any restriction, and if you let z=x+iy and take the modulus of both sides, you should notice that LHS=RHS.

 

[Mumma]

All points on argand diagram. The Z,z will always be an equal distance away from (0,2). Remember that Z is z reflected along the x (real) axis.