Answer: [tex]5+i[/tex]
Step-by-step explanation:
By definition, you know that the Complex numbers have the following form:
[tex]a+bi[/tex]
Where "a" and "b" are real numbers and "i" is the imaginary unit (Remember that [tex]i=\sqrt{-1}[/tex])
Having a polynomial P(x) with real coefficients, the Complex Conjugates rTheorem states that if [tex]a + bi[/tex] is a root of the the polynomial, then its complex conjugate [tex]a- bi[/tex] is also a root of the polynomial.
In other words, this Theorem states that the complex roots always appear in conjugate pairs.
Based on this, if you have the following root of a function:
[tex]5-i[/tex]
Then, its complex conjugate is also root of a function. This is:
[tex]5+i[/tex]
