Question

How do you find all the complex roots of `x^2 + 8x + 21=0`?

Answer 1

Rewrite this as follows

#x^2+8x+16+5=0=>(x+4)^2=-5=>(x+4)^2=5i^2=> x_1=-4+sqrt5*i , x_2=-4-sqrt5*i#

where `i` is the imaginary unit with `i^2=-1`