## anonymous one year ago 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

1. anonymous

I was thinking A or C because wouldnt the opposite also be a root

2. zepdrix

Yes :) Very good! Complex roots always come in conjugate pairs. The conjugate is when you switch only the sign on the complex number.

3. zepdrix

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

4. zepdrix

So which one are you leaning towards? A or C? :)

5. anonymous

Now that I take a second look, Im thinking C? Because the + becomes - and the -3 is just 3

6. zepdrix

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.

7. anonymous

oh! So A! That makes sense.

8. zepdrix

yay team \c:/