How do you find all additional roots given the roots #-4i# and #6-i#?
If these are roots of a polynomial equation with Real coefficients, then their conjugates,
If a polynomial equation has Real coefficients, then any Complex roots will occur in Complex conjugate pairs.
The Complex conjugate of
So in our example,
The same is true of many equations involving functions with Real coefficients too, but breaks down in some cases involving
#x = sqrt(-1)#
Which has only Real coefficients and root