Complex (1 Viewer)

[letsdie45]

Hi can someone explain how to sketch

1. | z - 3i | > | z + 2 |

2. w is a complex number and z is restricted as indicated.
w = (z-2i)/(1-z) , |z| = 2


Thanks

 

[Aquawhite]

I imagine that | z - 3i | is the same as | z + 2 | but looking at the changes to Re z and Im z.... | z - 3i | would be 3 units down on the polar plane (Argand diagram) and | z + 2 | would be 2 unit to the right on the Argand diagram.

I havn't had to graph things exactly like this yet (thanks to the delays of the HSC this year >_<)... I hope it helps.

 

[Official]

Hi can someone explain how to sketch

1. | z - 3i | > | z + 2 |

2. w is a complex number and z is restricted as indicated.
w = (z-2i)/(1-z) , |z| = 2


Thanks

For 1., you have to understand the form.
for |z - z1| = |z - z2|,
z describes the perpendicular bisector of the line joining the two points z = z1 and z = z2.

So on your Argand Diagram, plot A(3i) and B(-2) and find the midpoint of the line AB. Draw a dotted line that cuts through this midpoint, which is perpendicular to AB. This line is the locus for z for |z-3i| = |z+2|. Shade the region which satisfies the condition by subbing in a value on either side of the line.

 

[letsdie45]

ok thanks! i got 1, any ideas for 2. ?

 

[untouchablecuz]

 

[letsdie45]

Ohh ok thanks