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.

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) (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)
RELATED QUESTIONS
Find a fourth-degree polynomial function with zeros 1,-1, i and - i. Write the function (answered by solver91311)

Please someone help me understand how to do these problems. Please show all your work so... (answered by josgarithmetic)

Find a polynomial of least degree with integer coefficients that has the given zeros.... (answered by ikleyn)

suppose that a polynomial function of degree 5 with rational coefficients has 2, -SQR... (answered by josgarithmetic)

Find a polynomial function of least degree with integer coefficients that has the given... (answered by ikleyn)

A polynomial function f(x) with real coefficients has the given degree, zeros, and... (answered by Solver92311,Edwin McCravy)

Find all the zeros of the function and write the function in factored form, show all... (answered by josgarithmetic)

Write a polynomial function of minimum degree with real coefficents whose zeros include... (answered by jsmallt9)

find additional zeros for a function with degree 5 and the following zeros 2, -i,... (answered by Fombitz)