According to the Complex Conjugate Root Theorem, if a+bi is a root of a quadratic equation, then __blank__ is also a root of the equation. Which expression correctly completes the previous sentence?

a-bi

a+bi

-a-bi

-a+bi

a-bi

Step-by-step explanation:

If a quadratic equation lx^2+mx+n=0 has one imaginary root as a+bi then the other root is the conjugate of a+bi = a-bi

Because we have l, m and n are real numbers and they are the coefficients.

Sum of roots = a+bi + second root = - m/l

When - m/l is real because the ratio of two real numbers, left side also has to be real.

Since bi is one imaginary term already there other root should have - bi in it so that the sum becomes real.

i. e. other root will be of the form c-bi for some real c.

Now product of roots = (a+bi) (c-bi) = n/l

Since right side is real, left side also must be real.

i. e. imaginary part = 0

bi (a-c) = 0

Or a = c

i. e. other root c-bi = a-bi

Hence proved.