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# Further Complex Numbers

Maths and statistics discussion, revision, exam and homework help.

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1. Further Complex Numbers
Im stuck on this would appreciate any help

For part b,i just work
then i dont know what is the value of k
thanks
2. Re: Further Complex Numbers
I think you've got the gist of it, now just change the value of k while keeping in mind the range of theta allowed. i.e. from k = 0,1,2,-1.
Oh and put them into the appropriate exponential form.
Last edited by JohnyTheLad; 08-08-2012 at 11:24.
3. Re: Further Complex Numbers
(Original post by JohnyTheLad)
I think you've got the gist of it, now just change the value of k while keeping in mind the range of theta allowed. i.e. from k = 0,1,2,-1.
Oh and put them into the appropriate exponential form.
is the value of k random?
and how did i know that there are only 3 roots?
Last edited by 041087; 08-08-2012 at 14:06.
4. Re: Further Complex Numbers
The value of K could be anything, it depends on the range of theta required by the question. If you plot the roots on an argand diagram you will see that the points are equally spaced apart and if you plot more, the roots will start repeating.

This question is a bit iffy for me, as the number of distinct roots are normally equal to the power of Z. i.e. if you have z squared, you will have 2 distinct roots.
5. Re: Further Complex Numbers
In the part b) you have got ((pi/6 + 2kpi)/ (3/4)), you need to replace the (3/4) with 4/3 which is on the root 8. Then use k = -2, -1, 0, 1, 2 to get values for theta in range.
6. Re: Further Complex Numbers
(Original post by JohnyTheLad)
The value of K could be anything, it depends on the range of theta required by the question. If you plot the roots on an argand diagram you will see that the points are equally spaced apart and if you plot more, the roots will start repeating.

This question is a bit iffy for me, as the number of distinct roots are normally equal to the power of Z. i.e. if you have z squared, you will have 2 distinct roots.
yep, i know it but this case is 3/4.
then ive no ideal what k is
7. Re: Further Complex Numbers
(Original post by mazboy008)
In the part b) you have got ((pi/6 + 2kpi)/ (3/4)), you need to replace the (3/4) with 4/3 which is on the root 8. Then use k = -2, -1, 0, 1, 2 to get values for theta in range.
how do u know to use k = -2, -1, 0, 1, 2?
in the answer, there are only three roots.
if i use k = -2, -1, 0, 1, 2,
then five roots will be given
8. Re: Further Complex Numbers
The range of theta is, -pi < theta <= pi, now just plug in values of k that gives an angle that is within the range.
9. Re: Further Complex Numbers
(Original post by JohnyTheLad)
The range of theta is, -pi < theta <= pi, now just plug in values of k that gives an angle that is within the range.
I JUST FOUND A EASY WAY TO ACCEPT
THANKS

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Last updated: August 9, 2012
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