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Complex numbers VI

Punch

New member
Jan 29, 2012
23
Sketch on an Argand diagram the set of points satisfying both |z-4i|<=\sqrt{5} and \frac{\pi}{4}<=arg(z+4)<=\frac{\pi}{2}.

I have already sketched the 2 loci. The problem lies in the following part.

Hence find the least value of |z-2\sqrt{2}-4i|. Find, in exact form, the complex number z_1 represented by the point P that gives this least value.
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
Hence find the least value of |z-2\sqrt{2}-4i|.
Over which set of z? The intersection defined in the first part? It seems that you need to find the shortest distance from a point to a semi-disk.

Why don't you wrap the [tex]...[/tex] tags around your formulas?
 

Punch

New member
Jan 29, 2012
23
Over which set of z? The intersection defined in the first part? It seems that you need to find the shortest distance from a point to a semi-disk.

Why don't you wrap the \(z_1\) tags around your formulas?
Yes, how do I then find the complex number [tex]z_1[/tex] in the following part?

I tried using the latex but they didnt seem to work
 

Evgeny.Makarov

Well-known member
MHB Math Scholar
Jan 30, 2012
2,492
Yes, how do I then find the complex number [tex]z_1[/tex] in the following part?
See the following picture.



I tried using the latex but they didnt seem to work
Type [tex]\frac{\pi}{4}\le\arg(z+4)\le\frac{\pi}{2}[/tex] to get [tex]\frac{\pi}{4}\le\arg(z+4)\le\frac{\pi}{2}[/tex].