# Complex number $|z-w|$

On an Argand diagram, sketch the locus representing complex numbers satisfying $|z + i| = 1$ and the locus representing complex numbers w satisfying $\arg(w − 2) = 3\pi/4$.
Find the least value of $|z − w|$ for points on these loci.

I correctly sketch the Argand but how to find $|z-w|$, how to solve this, do i need to find the intersection between the 2 sketch...

• just edited the pie – Arodi007 Oct 22 '14 at 16:39
• Do you know that $|z-w|$ is simply the geometric distance between two points in the diagram? If you have a sketch showing the two sets, it should be immediately obvious where the shortest distance between them is. – Henning Makholm Oct 22 '14 at 16:40
• But how to calculate the distance ?? – Arodi007 Oct 22 '14 at 16:42
• x @Arodio: You don't need to calculate it. It should be clearly visible on your sketch how far it is. – Henning Makholm Oct 22 '14 at 16:48
• Are you assuming in $\;|z-w|\;$ that $\;z\;$ is on the circle $\;|z+i|=1\;$, and that $\;w\;$ is on the line $\;\arg(w-2)=\frac{3\pi}4\;$ ? – Timbuc Oct 22 '14 at 17:06