SOLUTION: Find a fourth-degree function with the zeros 1,-1, i and -i. Write the function in factored form. Please show all your steps. Thank you in advance.

Algebra ->  Test -> SOLUTION: Find a fourth-degree function with the zeros 1,-1, i and -i. Write the function in factored form. Please show all your steps. Thank you in advance.       Log On


   

Question 705365: Find a fourth-degree function with the zeros 1,-1, i and -i. Write the function in factored form.
Please show all your steps. Thank you in advance.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x = i or x = -i

x^2 = i^2 or x^2 = (-i)^2

x^2 = i^2 or x^2 = i^2

x^2 = i^2

x^2 = -1

x^2 + 1 = 0

x^2 + 1 is a factor

----------------------------------------

1 is a root, so x-1 is a factor

-1 is a root, so x+1 is a factor

Factors: x-1, x+1, x^2+1

Complete factorization: (x-1)(x+1)(x^2+1)