Question

Solve for x over the complex numbers.

Answer 1

Answer:

Step-by-step explanation:

Given x^2+4x+13=0, find the complex roots.  The best approach here is to use the quadratic formula.  Note that a = 1, b = 4 and c = 13.  

Thus, the discriminant, b^2 - 4ac, is (4)^2 - 4(1)(13) = 16 - 52 = -36, and the square root of that is plus or minus i√36, or  plus or minus 6i.  

plus or minus i√

Answer 2

Answer:

x = - 2 + 3i or x = - 2 - 3i

Step-by-step explanation:

Given quadratic equation,

$x^2 + 4x + 13=0$

By the quadratic formula,

$x=\frac{-4\pm \sqrt{4^2 - 4\times 1\times 13}}{2\times 1}$

$x=\frac{-4\pm \sqrt{16-52}}{2}$'

$x=\frac{-4\pm \sqrt{-36}}{2}$

$x=\frac{-4\pm 6i}{2}$

$x=-2\pm 3i$

Hence, the solution of the given equation,

x = - 2 + 3i or x = - 2 - 3i