Melody

Hi Michael and guest,

 

I thought it was interesting too.

Here is a proof.

 

You may like to watch this video on finding the arg(z)  first.  It is good.

 

but really |z| is just the distance Z is from (0,0) on the complex number plane

and

arg(z) is just the angle z makes with the positive real axis.  (at the origin of course) 

 

\(i^i=e^{-\pi/2}\\ proof\\ i^i=e^{[ln(i^i)]}\\ i^i=e^{i[ln(i)]}\\ \qquad\mbox{Now ln(z)=ln|z|+i*arg(z) so}\\ \qquad ln(i)=ln|i|+i*arg(i)\\ \qquad ln(i)=ln(1)+i*\frac{\pi}{2}\\ \qquad ln(i)=i*\frac{\pi}{2}\\ i^i=e^{i*i*\frac{\pi}{2}}\\ i^i=e^{-1*\frac{\pi}{2}}\\ i^i=e^{{\frac{-\pi}{2}}}\\ \)

.

 

Hi Rom and guests,

 

Thank you Rom for raising this issue for discussion. It is an issue that always concerns me.  

 

I have already written some of my views in my new "What is Happening Thread"

 

I do agree with you Rom.  I do not want question askers to be given just the answer, and most times I do not think that they should be given the whole answer either.  I am aware that i am often guity of doing this myself but I know it is not ideal.

 

I want the asker to be encouraged to interact with the anwerer.  Most of these askers are children.  Some are over confident and not very polite BUT others find us, as adults, and also mathematics, very intimidating.   Although I want the children to learn from us it must also be remembered that their communication and maths skills may be very rudimentary.  Even if they can learn what we are teaching they may not have the language (maths or English) to ask their question or respond to us in a completely correct manner. 

 

I am not disagreeing with you Rom.  You have expressed something that I have said many times.  I just want answerers to be sensitive to the askers.  Just offer them something that they may find helpful.  They may not get the full answer that they were hoping for but I do not want them going away and disliking maths and disliking maths teachers and feeling more inadequate than they did before they came.

 

I think that offering an appropriate "mathsisfun" or "purple math"s site or a you tube clip is often the VERY BEST answer that can be given.

 

In my "What is Happening " post I also said that I want answerers to work together and support each other.  If one is trying to teach a student and that means they have NOT given the student the entire answer I would like other answerers to consider very carefully before they race in and offer up a full solution.  I think that it is important that answerers do not undermine one another.

 

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WEll guest, I think that you have been answering a lot of questions and I really like your syle.  You are sensitive to how the child might be feeling but you rarely give full answers.  I think this is great.

I would vert much like you to become a member.  It is very ease.  You just need to choose a username and a password, that is it!  As a member you will become known and your answers will carry the credibility that you have earned.  Please think about it, it would be so much nicer if you had a name.  If for some reason you really do not want to do this, perhaps you could just put a name of your choice at the bottom of each of your posts. (But it would be much better if you joined up.)  

@@ What is Happening?  [Wrap4]    Sat  17/10/15     Sydney, Australia Time 11:04pm   ♪ ♫

 

 

Here are a couple of questions that caught my eye.

 

1)   Inverse Function Question.

This is a very simple question (high level) but it really made me think.   Thanks Rom.

http://web2.0calc.com/questions/maths-question_27015#r2

 

2)  Physics question concerning pressure.        Thanks CPhill

http://web2.0calc.com/questions/combined-gas-law-without-p2-t2

 

3) Also I was helping with a question and I dragged an old post of mine out of the dusty depths.  

This is a post that I urge upper high school students to peruse.  It is not very difficult and the concepts in it will be of great value to you.

http://web2.0calc.com/questions/how-do-you-find-a-power-function-that-is-graphed

 

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Now I would like to bring your attention to a post by Rom.  Thank you for posting this Rom 

 

i-m-concerned-that-we-are-just-doing-people-s-homework-for-them-that-s-no-way-to-encourage-people-to-actually-learn-the-math

 

 

Rom is concerned that answerers are answering but they are all too often NOT facilitating learning.

I intend to write a fuller response on Rom's thread, which is where all this discusion really belongs but I will say here, as I have said many times before that I believe that sometimes/often it is not helpful to give answers alone or to give fully worked answers.  And, it is definitely not helpful to answer a string of questions that are all of the same type.

Please try to work with the questioners.  Give them hints or suggestions.  Some of the very best answers are ones that refer the question asker to other resource sites like "mathsisfun", "purplemaths", or you tube clips.  These can often explain much better than we can!

Try and encourage the askers to interact with you.  If they won't responding to you it would almost always mean that they are not that interested.  You are best to leave it and move to the next question.

PLEASE if an answerer is trying to work with a question asker, for example, they may be requesting input from the asker, please consider hard before you give a full answer of your own.   This would undermine your fellow answerer and I think that it is important that answerers are seen to support one another.

I have more to say but it will be said on Rom's thread.

PLEASE RESPOND TO ROM.  We need to know what your attitude is.  Answerers need to understand each other so that we can work together with more efficiencey and harmony. :)

 

If you want to comment on teaching verses answering, please do so on Rom's thread.  If you want to comment on other matters please do so on the Lantern Thread.

 Thank you

 

I think that is the for my first entry in  "What is happening"  Enjoy your day