When the roots of a quadratic
equation are imaginary,
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).
If the discriminant is negative, when you solve your quadratic equation the
number under the radical sign in the quadratic formula is negative

forming complex roots.

Quadratic equation:
Quadratic formula:
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:
Express over the set of complex numbers,
look for a
negative value under the radical sign. 
Find the solution set of the given equation over the set of
complex numbers.
a = 3,
b = 4,
c = 10
Find the solution set of the given equation and express its
roots in a+bi form.

* Be sure to set the quadratic equation
equal to 0.
*
Arrange the terms of the equation from the
highest
exponent to the lowest exponent.

