Question 1095091
<br>If a polynomial has rational coefficients, then irrational and complex roots must occur in conjugate pairs.<br>
In case you aren't familiar with the term conjugate pairs, the conjugate of the complex number a+bi is a-bi; the conjugate of the irrational number a+b*sqrt(c) is a-b*sqrt(c).<br>
So in your example, with one root i, another root must be -i; and with one root 7*sqrt(11), another root must be -7*sqrt(11).<br>
The four roots are the conjugate pairs
(1) i and -i
(2) 7*sqrt(11) and -7*sqrt(11)