Monic polynomial of the lowest possible degree

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1. May 30, 2016

53Mark53

1. The problem statement, all variables and given/known data

A monic polynomial is a polynomial which has leading coefficient 1. Find the real, monic polynomial of the lowest possible degree which has zeros −1−2i,−2i and i. Use z as your variable.

3. The attempt at a solution

Would I just expand the zeros giving me

(z+1+2i)(z+2i)(z-i)

z^3+(1+3*I)*z^2+I*x+I*4+2

2. May 30, 2016

SammyS

Staff Emeritus
Don't forget: It's a real polynomial.

3. May 30, 2016

53Mark53

how would I make it real?

4. May 30, 2016

SteamKing

Staff Emeritus
Hint: what happened to the conjugates of the original roots?

5. May 31, 2016

53Mark53

Does that mean that I have to square the imaginary roots?

6. May 31, 2016

SteamKing

Staff Emeritus
What is the conjugate of the complex number, a + bi?

7. May 31, 2016

SammyS

Staff Emeritus
@53Mark53 ,
Here's what you said in a previous thread:
The same applies here, but now you have 3 complex roots, no two of which form a conjugate pair.

8. May 31, 2016

53Mark53

Thanks I got the right answer by using conjugate pairs