imaginary numbers x^2 + a^2 = 0 question

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September 15th 2012, 07:45 AM
ineedmathshelp

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
September 15th 2012, 07:52 AM
MarkFL

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

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

$x^2-(ai)^2=0$

$x^2=(ai)^2$

$x=\pm ai$
September 15th 2012, 07:55 AM
Plato

Re: imaginary numbers x^2 + a^2 = 0 question

Quote:

Originally Posted by ineedmathshelp

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 $i^2=-1$ .

$(ai)^2+a^2=a^2(i)^2+a=-a^2+a^2=0~.$
September 17th 2012, 03:29 AM
manoj9585

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.