Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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

Answer 5

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

Answer 6

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.

Answer 7

oh! So A! That makes sense.

Answer 8

yay team \c:/