# How do you find a polynomial with complex coefficients of the smallest possible degree for which i and 1+i are zeros and in which the coefficient of the highest power is 1?

##### 1 Answer

Oct 25, 2015

The polynomial is

#### Explanation:

Since using complex numbers a polynomial of degree

We can expand it into

I haven't fully understood the second question, but if you want the polynomial to have two solution, you can't go for a polynomial of degree one, because it will have only one solution.