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Distinct solution in complex plane Watch

1. Please help me to understand this , I've got the answer but not sure about it , the question is how many solutions in the complex plane does z^4 +1=0 have , express these solutions in the form a=a+bi , a and b should not involve triigs
2. (Original post by meme12)
Please help me to understand this , I've got the answer but not sure about it , the question is how many solutions in the complex plane does z^4 +1=0 have , express these solutions in the form a=a+bi , a and b should not involve triigs
What is your answer? Do you know the fundamental theorem of algebra?
3. (Original post by meme12)
Please help me to understand this , I've got the answer but not sure about it , the question is how many solutions in the complex plane does z^4 +1=0 have , express these solutions in the form a=a+bi , a and b should not involve triigs
look at similar question in the link

EDIT: too late so I am out...
4. The answer is as follows 4 solutions
z^4 =-1
e^pi i e^2pi i
z = e^2 pi i /4 pi i

a distinct solution
phi = +- pi/4+-3 pi /4

z1 = cos pi/4 +3 pi/4

etc
5. Ok ok thank you reply when you back , thanks have fun
6. (Original post by Principia)
What is your answer? Do you know the fundamental theorem of algebra?

7. (Original post by TeeEm)
look at similar question in the link

EDIT: too late so I am out...

Thanks thats really useful
8. (Original post by meme12)
Thanks thats really useful
no worries
9. (Original post by meme12)
Thanks thats really useful
It states that any polynomial of degree n has n roots in the complex plane. For the rest, do you know about roots of unity in an Argand Diagram?
10. Ill put in a pic of a text book that will help you greatly.

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11. This is literally everything you need.

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13. I don't know about the root any
14. (Original post by Principia)
It states that any polynomial of degree n has n roots in the complex plane. For the rest, do you know about roots of unity in an Argand Diagram?
The fundamental theorem of algebra doesn't help here, the equation could still only have 1 root (e.g. (z-1)^4=0).
15. (Original post by james22)
The fundamental theorem of algebra doesn't help here, the equation could still only have 1 root (e.g. (z-1)^4=0).
What is roots of unity
16. (Original post by meme12)
What is roots of unity
"nth roots of unity" are those (complex) numbers which when raised to the power n give you 1.

Are you studying A level or at university or some other course?

If you have z^4 + 1 = 0 that is basically the same as z^4 = -1 so you need the 4th roots of -1. Have you come across the fact that a number (apart from 0) has 2 square roots, 3 cube roots, 4 fourth roots etc?
17. (Original post by meme12)
What is roots of unity
Everything is explained in the images i have posted.
18. (Original post by davros)
"nth roots of unity" are those (complex) numbers which when raised to the power n give you 1.

Are you studying A level or at university or some other course?

If you have z^4 + 1 = 0 that is basically the same as z^4 = -1 so you need the 4th roots of -1. Have you come across the fact that a number (apart from 0) has 2 square roots, 3 cube roots, 4 fourth roots etc?

Hi , I am studying at university
19. (Original post by meme12)
Hi , I am studying at university
OK

Have you sorted this question out now - do you understand what it is asking?
20. Yes I did similar one too , is it right
z3-8i=o
will be = 8 e^i(pi/2+2npi)
= 8 e^i pi/2(1+4npi)
z0= 8(cos pi/2+isinpi/2)

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Updated: February 4, 2015
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