Complex Numbers

[Aladdin]

To every complex number , z different from -i . assign

f(z) = \(\displaystyle \frac{iz}{z+i}\)

Denote by M the point of the plane with affix z .

A) a) Find the coordinates of the point B whose affix z0 is the solution of the equation f(z0)= 1 + 2i.

Work !

Affix of B is z0 = xB + iyB

f(z0) = yB = 1 + 2i ..

From the question : Solution : means that if I replace the values I will get zero ...

 

[tkhunny]

What does "affix" mean in this context. Are you using a translation program or am I just missing it?

 

[Aladdin]

What does "affix" mean in this context. Are you using a translation program or am I just missing it?

Denote by M the point of the plane with affix z .

Point M is the image of z .....

But z is the pre-image of M ...

 

[Aladdin]

I got the answer ... Thank You

 

[tkhunny]

You're not going to share?

 

[Aladdin]

You're not going to share?

Ohh , Sorry tkhunny ..

Solution : \(\displaystyle \frac{iz0}{z0+i}= 1 + 2i\)

He continues expanding and simplifing : to reach , z0 = 1/2 - 3/2i

So B ( 1/2 , -3/2 ) :wink:

 

[tkhunny]

Time for me to update, I guess. Anyone with an historical persepective of the word "affix"?

 

[mmm4444bot]

… Anyone with an historical persepective of the word "affix"?

I have an historical perspective of discussing "Lebanese-thingy" math terminology with Alladin, if you think that would "help".

 

[Aladdin]

Re:

… Anyone with an historical persepective of the word "affix"?

I have an historical perspective of discussing "Lebanese-thingy" math terminology with Alladin, if you think that would "help".

C'mon Mark --- Don't you what affix means !

 

[mmm4444bot]

... Don't you what affix means [?]

I know six definitions, but none of them make sense to me with regard to your usage:

"the point of the plane with affix z"

In this quoted statement, I cannot even determine if "affix z" applies to the point versus the plane.

How about you tell us what it means (even though doing so might open a can of worms).

 

[Aladdin]

Re:

How about you tell us what it means (even though doing so might open a can of worms).

As we ALL know that every complex number has(have) an image on the plane (xoy) ...

Let z = 2 + i The image or affix of z is Point M( 2,1 ) .

z is the pre-image of M ...

I think you know these informations !

 

[mmm4444bot]

…The image or affix of z …

This tells me that you consider "affix" and "image" to be synonomous, as used in your original post.

Am I correct ?

 

[Aladdin]

Re:

…The image or affix of z …

This tells me that you consider "affix" and "image" to be synonomous, as used in your original post.

Am I correct ?

Ohh sorry Mark , Z is the affix of M -- M is the image of z ....( Clear Now )

 

[tkhunny]

That was clear some time ago.

What is not clear is the purpose of the additional word (affix) if there already exists a perfectly good word (image).

Is there an authoritative publication that evangelizes the use of "affix"? Perhaps a cultural difference of some sort?

 

[Deleted member 4993]

I suppose - that is one of the legacies of translation - I assume from French - Dennis????