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Math Help - imaginary numbers x^2 + a^2 = 0 question

  1. #1
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    imaginary numbers x^2 + a^2 = 0 question

    my edexcel further maths book says i need to solve this equation giving the answer in terms of the positive number a.
    x^2 + a^2 = 0.

    the answer in the back of the text book is x = + or - ai
    but i dont see how i can get this answer

    could someone please explain
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  2. #2
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    Re: imaginary numbers x^2 + a^2 = 0 question

    Whenever you have the square root of a negative value, you may change the sign under the radical and place an i outside the radical as a factor in its place.

    Another way to look at it is:

    x^2+a^2=0

    x^2-(-1)a^2=0

    Since i^2=-1 we may write

    x^2-i^2a^2=0

    x^2-(ai)^2=0

    x^2=(ai)^2

    x=\pm ai
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  3. #3
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    Re: imaginary numbers x^2 + a^2 = 0 question

    Quote Originally Posted by ineedmathshelp View Post
    my edexcel further maths book says i need to solve this equation giving the answer in terms of the positive number a.
    x^2 + a^2 = 0.
    the answer in the back of the text book is x = + or - ai
    but i dont see how i can get this answer
    could someone please explain
    For every real number a it is true that a^2\ge 0~.
    Therefore, there is no real solution for x^2+a^2=0.

    Thus concept of complex numbers was developed. We introduce the number i to the number system.
    i is a solution to x^2+1=0. So i^2=-1.

    (ai)^2+a^2=a^2(i)^2+a=-a^2+a^2=0~.
    Thanks from ineedmathshelp
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  4. #4
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    Re: imaginary numbers x^2 + a^2 = 0 question

    Yes, this is a complex number problem where i refers to iota, a imaginary number which is equal to √ -1. it is introduce to solve this type of problems where √ (negative number) occur.
    Last edited by skeeter; September 17th 2012 at 04:46 AM.
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