complex number

fm_hlp · 2013-06-02 00:32:17

By writing the equation

in the form

show that its roots are

please provide a step to step answer to teach me
i cant seem to solve

SteveB · 2013-06-02 03:20:00

I am not sure about this because I cannot do the very last bit of trigonometry but this is what I have got so far:

Using a right angled triangle in the Argand diagram:

Use the rule of multiplying by the complex conjugate pair:

Using standard trigonometric results we need this in terms of cot(A/2):

I have put in the minus sign in now. Well spotted anonimnystefy.
k = 0 is not a solution I agree Stefy, but why does my answer not work for k = 0 ?

EDIT: I now can see that cot(0) is not possible. Given that cot X = 1/(tan X) if X=0 then we have a division by zero.
Therefore the argument is not valid for this case.

Last edited by SteveB (2013-06-02 18:28:32)

anonimnystefy · 2013-06-02 04:17:50

Hi SteveB

Have you tried using the half-angle formulas for sine and cosine? (the answer provided has k*pi/5, not 2*k*pi/5 )

SteveB · 2013-06-02 04:44:51

I was working on those formulas as you were writing that post.
I think it works and produces the right result.
There are 5 solutions.

anonimnystefy · 2013-06-02 04:55:14

In this steps you lose s minus sign:

There are 4 solutions. k=0 is not a solution.

Last edited by anonimnystefy (2013-06-02 04:59:15)

SteveB · 2013-06-02 05:00:46

Yes. I agree. If you let k=0 then z = 1
Obviously (1 + 1)/1 = 2
So this cannot give us 1 when raised to the power of 5.
Why does my algebraic argument not work for k = 0
Usually a fifth root gives us five solutions. (????)

I can see your point about the negative sign as well .....

Last edited by SteveB (2013-06-02 05:03:40)

fm_hlp · 2013-06-02 05:03:50

wow
thanks a lot

anonimnystefy · 2013-06-02 05:04:35

Well, actually, when k=0, z is not defined (cot(0)=not defined). But, the first troubles with k=0 begin when we take the reciprocal of both sides of "1/z=..." .

Last edited by anonimnystefy (2013-06-02 05:05:28)

SteveB · 2013-06-02 05:10:48

Thanks anonimnystefy. I thought there might be a division by zero somewhere !!

fm_hlp · 2013-06-02 05:12:37

its a polynomial of power 4 as it simplifies to

anonimnystefy · 2013-06-02 05:29:14

fm_hlp wrote:

its a polynomial of power 4 as it simplifies to

That is not correct.

SteveB wrote:

Thanks anonimnystefy. I thought there might be a division by zero somewhere !!

You're welcome!

Last edited by anonimnystefy (2013-06-02 05:29:43)

Bob · 2013-06-02 05:38:19

hi Stefy

Why isn't it correct?

Bob

anonimnystefy · 2013-06-02 05:40:49

Oh, sorry. I didn't understand what he wanted to say. And, anyway, using that would be very hard for a hand method.

Math Is Fun Forum

#1 2013-06-02 00:32:17

complex number

#2 2013-06-02 03:20:00

Re: complex number

#3 2013-06-02 04:17:50

Re: complex number

#4 2013-06-02 04:44:51

Re: complex number

#5 2013-06-02 04:55:14

Re: complex number

#6 2013-06-02 05:00:46

Re: complex number

#7 2013-06-02 05:03:50

Re: complex number

#8 2013-06-02 05:04:35

Re: complex number

#9 2013-06-02 05:10:48

Re: complex number

#10 2013-06-02 05:12:37

Re: complex number

#11 2013-06-02 05:29:14

Re: complex number

#12 2013-06-02 05:38:19

Re: complex number

#13 2013-06-02 05:40:49

Re: complex number

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