Post by: paotra on September 12, 2010, 05:54:44 pm
a. z^2 + 4
b. z^2 - 2aiz + 1
c. z^2 - 2z + 1 + a^2
d. z^2 - 4
e. z^2 + 2z + 1 - a^2
How come we just can't simply do (z-1+ai)(z-2) ? isn't that also a quadratic?
All suggestions are welcome, thanks :)
Post by: vea on September 12, 2010, 06:02:11 pm
Should there be it's conjugate of
If yes, then the quadratic factor should be
Post by: paotra on September 12, 2010, 06:06:10 pm
Post by: vea on September 12, 2010, 06:28:37 pm
Post by: jimmy999 on September 12, 2010, 07:07:07 pm
It is C, however how come (z-1+ai)(z-2) is not considered? Is it only because in this case the answers do not have (z-1+ai)(z-2)?
You are correct in thinking that is a quadratic factor. In fact there are 3 different quadratic factors, it just depends on which linear factors you choose. For this question, only one of them is a quadratic factor so you have to pick C.
I think they also want the quadratic factor to be real- I'm not too sure about this though.If the solutions are in complex conjugates, then the quadratic factor must be real as the conjugate root theorem only holds for real coefficients