Question 695868
To solve a quadratic equation for complex solutions, you work just as you do for real solutions,
except that you go further than the point where you would say the equation has no real solutions,
because a negative number cannot be the square of a real number,
but it is the square of a complex number.
 
{{{(x+5)^2=-36}}} <--> {{{(x+5)^2=(-1)(6^2)}}}
The only real (and complex) numbers that squared equal {{{36=6^2}}} are {{{-6}}} and {{{6}}}
The only complex numbers that squared equal {{{-1}}} are {{{-i}}} and {{{i}}}
So, the only complex numbers that squared equal {{{-36=(-1)(6^2)}}} are {{{-6i}}} and {{{6i}}}.
So, either {{{x+5=-6i}}} <--> {{{highlight(x=-5-6i)}}},
or {{{x+5=6i}}} <--> {{{highlight(x=-5+6i)}}}