## Complex Numbers : Argand Diagram

On an Argand diagram, sketch the region R where the following inequalities are satisfied:

l iz + 1 + 3i l less than or equal to 3

How do you draw this loci?
Do i manipulate the equation?

if so i got this :

l z - ( -3 + i ) l less than or equal to 3i

But how in the world do you draw this?

And is :

( l iz + 1 + 3i l less than or equal to 3 )= ( l z* + 1 + 3i l less than or equal to 3)

If so can is it possible to draw the z* loci and relate it to z's loci.

Any help will be greatly appreciated. Thanks.
 PhysOrg.com science news on PhysOrg.com >> Ants and carnivorous plants conspire for mutualistic feeding>> Forecast for Titan: Wild weather could be ahead>> Researchers stitch defects into the world's thinnest semiconductor
 z is some complex number of the form x+iy. What is the modulus of l iz + 1 + 3i l? (Hint: Simplify iz + 1 + 3i to the form A+iB and then find the modulus.)
 If i am going to let z = x + yi Then i will get the following results : l (1-y) + (3 + x)i l Less than or = 3 if so, do i draw a circle with radius 3, centre ( -1, -3) ? So how this feels wrong.

Recognitions:
Homework Help

## Complex Numbers : Argand Diagram

 Quote by Delzac If i am going to let z = x + yi Then i will get the following results : l (1-y) + (3 + x)i l Less than or = 3 if so, do i draw a circle with radius 3, centre ( -1, -3) ? So how this feels wrong.
It should be a circle with radius 3, centre (-3,1)... what's the modulus of l (1-y) + (3 + x)i l ?

Recognitions:
Homework Help
 Quote by Delzac On an Argand diagram, sketch the region R where the following inequalities are satisfied: l iz + 1 + 3i l less than or equal to 3 How do you draw this loci? Do i manipulate the equation? if so i got this : l z - ( -3 + i ) l less than or equal to 3i
You should have l z - ( -3 + i ) l less than or equal to 3. so that's just a circle (and everything inside the circle) centered at -3+i.
 k i got it, thanks.