Answer: B) 4 - 7i
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Step-by-step explanation:
When you have a quadratic in the form ax^2 + bx + c = 0, where a,b,c are real numbers, then a negative discriminant leads to having a pair of complex roots. The roots come in conjugate pairs meaning that p+qi is one root while p-qi is the other root. The p,q are real numbers.
In the case of 4+7i being one root, we have p = 4 and q = 7, since it matches with p+qi. The other root must be 4-7i since it matches with p-qi.
In short, we flip the plus to a minus when going from 4+7i to 4-7i. All of this applies when we have a,b,c as real numbers.
If we allowed a,b,c to be complex numbers, then the roots may not necessarily come in conjugate pairs.