Square root of a negative number

[stopandthink]

How do i find the square root of a negative number....?

 

Lets say [math] \sqrt -4 [/math]

My calculator gives me the answer 0

 

is it because [math] -a(-a)=+b [/math] where a equals -2(i assume -2 should be its squared root but its not)

Edited October 15, 2012 by stopandthink

[ydoaPs]

Well, that's a bad calculator. It should either give you an error or the correct answer (which 0 is not).

 

To take a square root of a negative number, you need to factor out a [math]\sqrt{(-1)}[/math]. Since -1=i², the answer is 2i.

[stopandthink]

I see now. thaks

[zorro]

You have entered the world of imaginary numbers. (imagine that).

 

 

http://en.wikipedia.org/wiki/Imaginary_number

An imaginary number is a number whose square is less than or equal to zero.^[1] For example, is an imaginary number and its square is . An imaginary number can be written as a real number multiplied by the imaginary unit , which is defined by its property .^[2]

 

An imaginary number can be added to a real number to form a complex number of the form , where and are called, respectively, the real part and the imaginary part of the complex number. Imaginary numbers can therefore be thought of as complex numbers whose real part is zero. The name "imaginary number" was coined in the 17th century as a derogatory term, as such numbers were regarded by some as fictitious or useless, but today they have a variety of essential, concrete applications in science and engineering.

 

zorro