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Oh, sorry. I didn't understand what he wanted to say. And, anyway, using that would be very hard for a hand method.
That is not correct.
its a polynomial of power 4 as it simplifies to
Thanks anonimnystefy. I thought there might be a division by zero somewhere !!
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=..." .
Yes. I agree. If you let k=0 then z = 1
In this steps you lose s minus sign:
There are 4 solutions. k=0 is not a solution.
I was working on those formulas as you were writing that post.
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.
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