If f(x) = 1 - x, which value is equivalent to |f(i)|?

Options:
A. 0
B. 1
C. √2
D. √(-1)

To solve for ∣ f ( i ) ∣ where f ( x ) = 1 − x , we need to find the absolute value of the function when the input is the imaginary unit i .
Here's the step-by-step process:

Substitute i into the function: f ( i ) = 1 − i

Find the absolute value of a complex number:



For a complex number a + bi , the absolute value is given by: ∣ a + bi ∣ = a 2 + b 2 ​


Apply the formula to f ( i ) = 1 − i :


Here, a = 1 and b = − 1 .

So, the absolute value is: ∣1 − i ∣ = 1 2 + ( − 1 ) 2 ​ = 1 + 1 ​ = 2 ​


Thus, the value of ∣ f ( i ) ∣ is 2 ​ .
The correct multiple-choice option is (C) 2 ​ .

Answered by OliviaLunaGracy | 2025-07-06

The value of |f(i)| is √2. Therefore, the correct multiple-choice option is (C) √2.
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Answered by OliviaLunaGracy | 2025-07-18