Complex Numbers : Argand Diagram

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

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.

neutrino

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.)

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.

learningphysics

It should be a circle with radius 3, centre (-3,1)... what's the modulus of l (1-y) + (3 + x)i l ?

learningphysics

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.

Delzac

k i got it, thanks.