Answer:
We just need to evaluate and get f(2i)=0, f(-2i)=0.
Step-by-step explanation:
Since [tex]i^2=-1[/tex], then [tex]i^3=i^2i=-i[/tex], and we can apply this when we evaluate [tex]f(x) =x^3 + 4x[/tex] for 2i and -2i.
First we have:
[tex]f(2i) =(2i)^3 + 4(2i)=2^3i^3+8i=8(-i)+8i=0[/tex]
Which shows that 2i is a zero of f(x).
Then we have:
[tex]f(-2i) =(-2i)^3 + 4(-2i)=(-2)^3i^3-8i=-8(-i)-8i=8i-8i=0[/tex]
Which shows that -2i is a zero of f(x).
