complex number system?

Question

solve using the complex number system:

x^2 + 4x +8 = 0

please help explain, thanks

Answer 1

Well, if you gun that trough the quadratic formula you get
x = -2 + 2*sqrt(-1)
and
x = -2 - 2*sqrt(-1)

The square root of a negative number is not a real number but rather an imaginary number
see: http://en.wikipedia.org/wiki/Imaginary_number
and http://en.wikipedia.org/wiki/Real_numbers

A complex number involves both a real number and an imaginary number. And when it comes to imaginary numbers the square root of -1 is simply called "i".

So,
x = -2 + 2i
and
x = -2 - 2i

If you look at the graph of the original equation, you'll see it never crosses the x-axis, resulting in x-intercepts that are "complex" as opposed to a "real".

Answer 2

If the term b^2-4ac (a=coeff of x^2 term, etc) is less than 0, you will have two complex number roots. Otherwise, the solution works the same as any other solution. By completing the square,
x^2 + 4x + 4 = -4
(x+2)^2 = +/- 2i
x = -2 +/- 2i.

Answer 3

The complex number system contains imaginary numbers (as opposed to "real" numbers) and have a notation to denote the square root of a negative number eventhough we all know that in the real numbers no number multiplied by itself will give a negative answer--thus imaginary numbers were invented. In mathematics, when the notation cannot represent the answer we simply create new notation there for "the square root of negative one" was named "i".

Answer 4

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Answer 5

x^2 + 4x + 8 = 0
x = {-4+-SQRT[(4^2)-4(1)(8)]} / 2(1)
x = [-4+-SQRT(-16)] / 2
x = [-4+-4i] / 2
x = -2 +-2i

Note that SQRT(-1) = i

Answer 6

x = [- 4 ± √(16 - 32)] / 2
x = [- 4 ± √(- 16)] / 2
x = [- 4 ± √(16 i²] / 2
x = [- 4 ± 4 i] / 2
x = - 2 ± 2i
x = - 2.(1 ± i )