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

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:

Since we may write

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

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.