complex number locus (1 Viewer)

[pLuvia]

Find the locus of

4. |z+2i| = 2|z-2i|
5. |z-3|+|z+3|=5
6. ||z+4i| - |z-4i|| = 6
7. (z+5i)/(z-2) is purly imaginary

 

[*fkr]

4. |z+2i| = 2|z-2i|
|x + (y+2) | = 2|x+(y-2) |
Sqrt( x2 + (y+2)2 ) = 2 sqrt( x2 + (y-2)2 )
x2 + y2 +4y + 4 = 4( x2 + y2 -4y +4 )
3x2 + 3y2 -20y + 12 = 0
X2 + y2 – 20/3y + 4 = 0
Complete square to find equation of circle

5. |z-3|+|z+3|=5
Is an ellipse but we’re not doing these until conics

7. (z+5i)/(z-2) is purly imaginary
(x + (y+5)i) / ((x-2) +iy)
Realise denominator
X(x-2) – ixy + (y+5)(x-2)I + (y+5)y / (x-2)2 + y2
As equation is purely imaginary….
X(x-2) = 0
And
Y(y+5) = 0
Solve from there

 

[pLuvia]

5. |z-3|+|z+3|=5
Is an ellipse but we’re not doing these until conics

The answer says it's a hyperbola

 

[PLooB]

|z - a| + |z + a| = b is an ellipse of focii the fixed points (-a,0) and (a.0) and end points + or - b/2

 

[pLuvia]

ok thanks