they always occur in conjugate pairs.
A root of an equation is a solution of that equation. 
If a quadratic equation with realnumber coefficients
has a negative discriminant,
then the two solutions to the equation are complex conjugates of each other.
(Remember that a negative number under a radical sign yields a complex number.)
The discriminant is the b^{2} 4ac part of the quadratic formula (the part under the radical sign). 
Quadratic equation:
Quadratic formula:
Example 1: 
Find the solution set of the given equation over the set of complex numbers.
a = 1, b = 10, c = 34
Pick out the coefficient values representing a, b, and c, and substitute into the quadratic formula, as you would do in the solution to any normal quadratic equation. Remember, when there is no number visible in front of the variable, the number 1 is there. 

HINT: When the directions say: 
Example 2: 
Find the solution set of the given equation over the set of complex numbers.
a = 3, b = 4, c = 10
Example 3: 
Find the solution set of the given equation and express its roots in a+bi form.
Source:
http://www.regentsprep.org/Regents/math/algtrig/ATE3/quadcomlesson.htm
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