Question

Someone please help me with this question.

Answer 1

Sketch the locus representing the complex numbers z satisfying |z+i|=1 and the locus representing the complex numbers w satisfying |w-2|=3 pi/4. Find the least value of |z-w| for points on these loci.

Answer 2

I have drawn the loci. Please tell me how to find the least value of |z-w|.

Answer 3

WHERE IS THE W???

Answer 4

The line I drew representing the angle 3 pi/ 4.

Answer 5

oh nm i was reading the w as a 3 im retarted

Answer 6

I don't know if the coloured lines are correct. That was just my attempt at solving it. :(

Answer 7

do you have the original?

Answer 8

Okay, I'll post it here.

Answer 9

Here it is with just the loci drawn.

Answer 10

and you are looking for what exactly?

Answer 11

I have to find the least value of |z-w|

Answer 12

alright

Answer 13

what lines is z and w

Answer 14

@amistre64

Answer 15

@emcrazy14 W is basically represents a line
having a slope of m1=tan(3pi/4)
a line which is perpendicular to this will be a line of slope m2=-(1/m1 )
form the line
now the shortest distance will be perpendicular to both the circle and the line W
and line perpendicular to circle will pass through center use it

Answer 16

The perpendicular to the circle should start at (0,0)?

Answer 17

no
but at (0,i)

Answer 18

I still didnot get it. Please can you explain it a bit more? @Aperogalics

Answer 19

How do you get a line out of this
|w-2|=3 pi/4
?

|w-2| means the "distance of the number w from the point 2 + 0i " is a constant (= 3pi/4 )
that would be a circle with radius 3pi/4 with center (2,0) on the complex plane.

Answer 20

Sorry, that's actually arg (w-2) = 3pi/4

Answer 21

So I have drawn a circle with centre (0,-i) and radius 1. And an angle representing 3pi/4 starting at (2,0)

Answer 22

If W really is the line you drew in, then you have