The Conjugate Pairs Theorem states that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. This tells us that if a + bi is a zero, then so is a – bi and vice-versa.
In this case the given zero is:
[tex]1+i[/tex]
The conjugate of the complex number 1 + i is:
[tex]1-i[/tex]
Therefore, by the Conjugate Pairs theorem the other zero is 1 - i
.
