Question

question evaluate: $i^{24}$ answer $i$ $-i$ $-1$ $1$

Explanation:

Step1: Recall the powers - of - i rule

The powers of the imaginary unit \(i\) have a cycle: \(i^1 = i\), \(i^2=-1\), \(i^3 = i^2\times i=-i\), \(i^4=(i^2)^2 = (-1)^2 = 1\).

Step2: Divide the exponent by 4

We want to find \(i^{24}\). Divide the exponent 24 by 4: \(\frac{24}{4}=6\) with a remainder of 0.

Step3: Determine the value of \(i^{24}\)

When the exponent of \(i\) is divisible by 4, \(i^n = 1\) (where \(n\) is a non - negative integer divisible by 4). Since 24 is divisible by 4, \(i^{24}=1\).

Answer:

1