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Distinct solution in complex plane

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

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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?
Reply 2
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TeeEm
19
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

http://www.madasmaths.com/archive/maths_booklets/further_topics/various/complex_numbers_part_2.pdf

EDIT: too late so I am out...
Reply 3
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Great444
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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
Reply 4
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Great444
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Ok ok thank you reply when you back , thanks have fun
Reply 5
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Great444
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Original post by Principia
What is your answer? Do you know the fundamental theorem of algebra?



I added the answer , no I dont
Reply 6
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Great444
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Original post by TeeEm



Thanks thats really useful:smile:
Reply 7
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TeeEm
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Original post by meme12
Thanks thats really useful:smile:


no worries
Original post by meme12
Thanks thats really useful:smile:


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?
Ill put in a pic of a text book that will help you greatly.


Posted from TSR Mobile
ImageUploadedByStudent Room1422647818.569693.jpgImageUploadedByStudent Room1422647839.759213.jpgImageUploadedByStudent Room1422647861.846956.jpgImageUploadedByStudent Room1422647874.870215.jpgImageUploadedByStudent Room1422647889.559711.jpg
This is literally everything you need.


Posted from TSR Mobile
Reply 11
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Great444
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No I don't am trying to read and answer , thank you thisis really helpful
Reply 12
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Great444
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I don't know about the root any
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).
Reply 14
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Great444
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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
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davros
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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?
Original post by meme12
What is roots of unity


Everything is explained in the images i have posted.
Reply 17
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Great444
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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
Reply 18
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davros
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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?
Reply 19
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Great444
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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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