Question

Find the remaining zeros of $f\left(x\right)$with real coefficients and given information.

The degree is 4 and zeros are role="math" localid="1646221442495" $i,1+i$

Short answer

The two remaining zeros of the polynomial are$-i,1-i$.

Step-by-step solution

Step 1. Given Information

The polynomial has degree 4 and two zeros are$i$and$1+i$.

Step 2. Concept

Conjugate Pair Theorem says that if a polynomial with degree $n$ with real coefficient, has one complex zero of the form $a+ib$ then the polynomial should have the conjugate pair of $a+ib$ that is $a-ib$ as another zero.

Step 3. Explanation

Since $f\left(x\right)$has coefficients that are real numbers, complex zeros appear as conjugate pairs.

It follows that $-i$, the conjugate of $i$, and $1-i$, the conjugate of $1+i$, are the two remaining zeros.