SOLUTION: Decide whether the given x-value is a zero of the function f(x)=x^3-4x^2+16x-64, x=4i

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Question 380109: Decide whether the given x-value is a zero of the function
f(x)=x^3-4x^2+16x-64, x=4i
Answer by kingme18(98) About Me  (Show Source):
You can put this solution on YOUR website!
If a number is a function's zero, that means that if you plug the number in, the result will be zero. For this function, we'll have to plug in 4i for all of the x'es and see if our result is 0.
Recall that i%5E2=-1, i%5E3=-i, and i%5E4=1
f%28x%29=x%5E3-4%2Ax%5E2%2B16%2Ax-64
f%284i%29=%284i%29%5E3-4%2A%284i%29%5E2%2B16%2A%284i%29-64
f%284i%29=4%5E3%2Ai%5E3-4%2A4%5E2%2Ai%5E2%2B16%2A4%2Ai-64
f%284i%29=64%2A%28-i%29-4%2A16%2A%28-1%29%2B64%2A%28i%29-64
f%284i%29=-64i%2B64%2B64i-64
Note that like terms do, in fact, cancel: -64i+64i=0 and 64-64=0
f%284i%29=0
Yes, 4i is a zero!