if $f(x)=x^{3}-2x^{2}$, which expression is equivalent to $f(i)$?\n-2 + i\n-2 - i\n2 + i\n2 - i

if $f(x)=x^{3}-2x^{2}$, which expression is equivalent to $f(i)$?\n-2 + i\n-2 - i\n2 + i\n2 - i

if $f(x)=x^{3}-2x^{2}$, which expression is equivalent to $f(i)$?\n-2 + i\n-2 - i\n2 + i\n2 - i

Answer

Explanation:

Step1: Substitute $x = i$ into $f(x)$

$f(i)=i^{3}-2i^{2}$

Step2: Recall the properties of $i$

We know that $i^{2}=-1$ and $i^{3}=i^{2}\cdot i=-i$. So $f(i)=-i - 2\times(-1)$

Step3: Simplify the expression

$f(i)=-i + 2=2 - i$

Answer:

$2 - i$