Complex number $|z-w|$

Asked Oct 22 '14 at 16:35

Active Sep 08 '19 at 15:32

Viewed 593 times

On an Argand diagram, sketch the locus representing complex numbers satisfying $|z + i| = 1$ and the locus representing complex numbers w satisfying $\arg(w − 2) = \dfrac{3\pi}{4}$.
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...

edited Sep 08 '19 at 15:32

Max Wong

asked Oct 22 '14 at 16:35

Arodi007

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. – hmakholm left over Monica Oct 22 '14 at 16:40
But how to calculate the distance ?? – Arodi007 Oct 22 '14 at 16:42
1

x @Arodio: You don't need to calculate it. It should be clearly visible on your sketch how far it is. – hmakholm left over Monica 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
Yes, z is on the circle and w on the line. – Arodi007 Oct 22 '14 at 17:08

Complex number $|z-w|$

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