Sorry i wrote the last question wrong, it was suppose to be written as:
information is given about the polynomial f(x) whose coefficients are real numbers. find the remaining zeros of f:
degree 4; zeros: i, 3+i
No problem! To find the remaining zeros of a polynomial given some of its zeros, we can use a property known as conjugate roots.
When a polynomial with real coefficients has a complex number as one of its roots, the conjugate of that complex number is also a root. In other words, if a + bi is a root of the polynomial, then a - bi is also a root.
In your case, the given zeros are i and 3 + i. Since i is a complex number, its conjugate -i is also a root. So, the remaining zero of the polynomial is -i.
Hence, the complete set of zeros for the polynomial f(x) is {i, 3 + i, -i}.