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    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?
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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
    look at similar question in the link

    http://www.madasmaths.com/archive/ma...ers_part_2.pdf

    EDIT: too late so I am out...
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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
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    Ok ok thank you reply when you back , thanks have fun
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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
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    (Original post by TeeEm)
    look at similar question in the link

    http://www.madasmaths.com/archive/ma...ers_part_2.pdf

    EDIT: too late so I am out...

    Thanks thats really useful
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    (Original post by meme12)
    Thanks thats really useful
    no worries
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    (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?
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    Ill put in a pic of a text book that will help you greatly.


    Posted from TSR Mobile
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    Name:  ImageUploadedByStudent Room1422647818.569693.jpg
Views: 86
Size:  111.2 KBName:  ImageUploadedByStudent Room1422647839.759213.jpg
Views: 78
Size:  120.3 KBName:  ImageUploadedByStudent Room1422647861.846956.jpg
Views: 78
Size:  115.2 KBName:  ImageUploadedByStudent Room1422647874.870215.jpg
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Size:  111.3 KBName:  ImageUploadedByStudent Room1422647889.559711.jpg
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    This is literally everything you need.


    Posted from TSR Mobile
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    No I don't am trying to read and answer , thank you thisis really helpful
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    I don't know about the root any
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    (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).
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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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    (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?
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    (Original post by meme12)
    What is roots of unity
    Everything is explained in the images i have posted.
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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
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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?
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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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