Question

What is the solution of the equation when solved over the complex numbers?


x^2+20=0


x = ____ or x = ____

Answer 1

Answer:

$x=+i\sqrt{20}\approx+4.472i$

$x=-i\sqrt{20}\approx-4.472i$

Step-by-step explanation:

Starting from $x^2+20=0$, we do $x^2=-20$, which means $x=\pm\sqrt{-20}$, which can be written as $x=\pm\sqrt{(-1)(20)}$, which gives us $x=\pm\sqrt{(-1)}\sqrt{(20)}$, which we know is $x=\pm i \sqrt{(20)}$, so our solutions are:

$x=+i\sqrt{(20)}$

$x=-i\sqrt{(20)}$

Which can be approximated to:

$x\approx+4.472i$

$x\approx-4.472i$