Complex no help (1 Viewer)

[darkphoenix]

ok, so i was revising complex no. and one question asks to find the locus of w= z-2i/1-z absolute value (z) =2
and the answer is a circle with radius: root 20/3 and center (-4/3, 2/3)
I don't get why my working doesn't work:
[] = absolute value
z-zw = z-2i
z(1+w)=w+2i
z= w+2i/1+w
2= [(w+2i)/(1+w)]
2[w+2i] = [1+w]
and use the distance formula to find the equation

Can someone explain with solutions to this, thanks

 

[RealiseNothing]

ok, so i was revising complex no. and one question asks to find the locus of w= z-2i/1-z absolute value (z) =2
and the answer is a circle with radius: root 20/3 and center (-4/3, 2/3)
I don't get why my working doesn't work:
[] = absolute value
z-zw = z-2i
z(1+w)=w+2i
z= w+2i/1+w
2= [(w+2i)/(1+w)]
2[w+2i] = [1+w]
and use the distance formula to find the equation

Can someone explain with solutions to this, thanks

The LHS shouldn't be z-zw. It should be w-wz.

 

[darkphoenix]

sorry that was a typo

 

[SpiralFlex]

Straight away you will know that this belongs to a family of the circles of Apollonius.




Let


Substituting and expanding,












Radius:

Centre:


Note: It is good to geometrically interpret what you are actually doing. Graphical software is suggested by Spiral for loci.

 

[darkphoenix]

Oh, thanks spi. I just realise my mistake in the distance formula part... sign can't even do 2u now