If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –3 – i –3i 3 – i 3i

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If –3 + i is a root of the polynomial function f(x), which of the following must also be a root of f(x)? –3 – i –3i 3 – i 3i

Mathematics
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I was thinking A or C because wouldnt the opposite also be a root
Yes :) Very good! Complex roots always come in `conjugate pairs`. The conjugate is when you switch only the sign on the `complex number`.
Example: The conjugate of \(\large\rm 2+i\) will be \(\large\rm 2-i\) Again, I only switch the sign of the imaginary part. Not complex part, i dunno why I said that the first time :) lol

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So which one are you leaning towards? A or C? :)
Now that I take a second look, Im thinking C? Because the + becomes - and the -3 is just 3
Wooooops! Remember what I was saying, you only switch the sign of the `imaginary component`. –3 + i So the \(\large\rm i\) becomes \(\large\rm -i\) nothing else should change though.
oh! So A! That makes sense.
yay team \c:/

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