Function of 6+7i and 6-7i

Question

Equation of function that has the solutions 6+7i and 6-7i

Answer 1

Try

 

f(x) = [x - (6 + 7i)][x - (6 - 7i)]

 

Expand f(x), group like terms, and get an expression with only real coefficients:

 

f(x) = x² - 12x + 85

 

Test the answer by setting

 

f(x) = 0 

 

and verify using the quadratic formula that the roots are indeed 6 ± 7i.