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

[Punch]

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]

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 $$...$$ tags around your formulas?

 

[Punch]

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

 

[Evgeny.Makarov]

Yes, how do I then find the complex number z_1 in the following part?

See the following picture.

I tried using the latex but they didnt seem to work

Type $$\frac{\pi}{4}\le\arg(z+4)\le\frac{\pi}{2}$$ to get \frac{\pi}{4}\le\arg(z+4)\le\frac{\pi}{2}.