MHB Complex Numbers VI: Finding Least Value of |z-2√2-4i|

Punch
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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.
 
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Punch said:
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?
 
Evgeny.Makarov said:
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 z_1 in the following part?

I tried using the latex but they didnt seem to work
 
Punch said:
Yes, how do I then find the complex number z_1 in the following part?
See the following picture.

argand.png


Punch said:
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 \frac{\pi}{4}\le\arg(z+4)\le\frac{\pi}{2}.
 

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