What Are Some Challenging Applications of Complex Numbers in Mathematics?

[Morchelloo]

Hello everyone. i got one interesting homework. So... i need write about complex numbers. I already found many materials for that homework but... i stuck in one interesting point. I must write a pretty complicated task(teaser). i must think that task myself.
Like simply task...z=a+bi---> 3+8i (complex nummber)
medium task...z=(-3+4i)/(2-i)
i need complicated task. now you know what i mean.. I must think question(example) and also to solve the problem(give answer).
It countains: 1) only complex numbers. 2) need to do-multiplication (z1*z2), distribution(z1/z2), counting(z1+z2), subtraction(z1-z2), evolution, also give answer in trigonometric form,(with cos, isin, grades, pii) algebraical form. and also write it to exponent form (e=).
but tangens(fii) i need get to the end in normal form. it means: if a is real nummber and bi(b) is number than tang=b/a it will be 1 (for 45 degrees) and so on...
can you write that example and write also solution for that in all ways. it must be pretty difficult.
If you still don't understand what i mean than give me please links to the math internet sites where i can myself find difficult tasks and answers for complex nummbers, where are examples of that kind of tasks(really difficult but in the end very simply answers).
I'll be very appreciative to human who helps me.. mathematics rullz-i only need advices and a little bit of help
thanks

 

[cristo]

I'm not sure I know what you mean by these "tasks". For example, what do you mean by this: z=a+bi---> 3+8i ? I presume for the second one you are asking to simplify z=(-3+4i)/(2-i).

If you google something like "exercises on complex numbers" you will come up with many such problem sets

 

[Morchelloo]

it's difficult to explain because i came from another country, i am not english people. And talk about maths in English-it is 2xhard...
Yes i mean simplify but this example... z=(-3+4i)/(2-i)... it is very easy. i need difficult than this one. i can say: i need something what i can't do alone. it is my homework. i have 2 weeks to end my homework. all is great but this is my problem...
Just give me example of pretty difficult task (z=...) + solutions of that and it will be very pleasent...

 

[matadorqk]

Here.

Hmm, well, these are some problems from my homework, tell me if they help.

This is one which I think involves around what you want:

Given that $$|z|=2\sqrt{5}$$ find the complex number z that satisfies the equation: $$\frac {25} {z} - \frac {15}{z^{*}}=1-8i$$

Now that you have the problem, solve for the answer :)

 

[Morchelloo]

it's pretty good but i need answer too.. )) Maybe someone can help me/us
and.. give me please links where i can found really difficult tasks with answers..
i want to learn something hard)

 

[malawi_glenn]

it's pretty good but i need answer too.. )) Maybe someone can help me/us
and.. give me please links where i can found really difficult tasks with answers..
i want to learn something hard)

Why don't you try to find the answer then see if it fits?

You can search on google for things like "old exams complex algebra" or similar til you find something.

 

[Morchelloo]

tnx friends. this forum rullz!

 

[cristo]

it's pretty good but i need answer too.. )) Maybe someone can help me/us
and.. give me please links where i can found really difficult tasks with answers..
i want to learn something hard)

Firstly, I seems a bit strange to me that you want "really hard" problems; problems so hard that you don't attempt them and just want the solution. Secondly, how would you know if the above question is "pretty good" (i.e. fits your requirements) if you don't have a solution to see how to do it!

I'm not sure what the exact homework brief is, but surely it would be better to do a simpler problem that you could handle, rather than a difficult one that you just copied the answer down.

 

[Morchelloo]

ok you don't understand me, but ok) for these questions(if you want to know answer what i mean) download icq and i explain you my thoughts. my icq nr. is written by my profile.

 

[matadorqk]

Solve it.

Firstly, I seems a bit strange to me that you want "really hard" problems; problems so hard that you don't attempt them and just want the solution. Secondly, how would you know if the above question is "pretty good" (i.e. fits your requirements) if you don't have a solution to see how to do it!

I'm not sure what the exact homework brief is, but surely it would be better to do a simpler problem that you could handle, rather than a difficult one that you just copied the answer down.

I agree. Morchello, the only way for you to learn is to try the problem. So take the problem I suggested, and show us how you would solve it. It seems you just want to finish your homework, without really doing anything but finding the answer online. Where's your enthusiasm for math :D! So I just suggested a problem, now how about you give a stab at it and try solving it?

 

[Morchelloo]

ok i understand the point :D i try, but not so soon.. i am very busy to another problems. actualy i am busy 24/7. i haven't real life "but life goes on" (2PAC) and one more thing. in a higher mathematics i have good marks/ratings. i just wanted to knew about something that i don't now yet!
Problem solved :) thx