Question

What is the value of $i^{99}$ (where $i$ is the imaginary unit)?

• A. 1
• B. $-1$
• C. $i$
• D. $-i$

Hint:

Powers of $i$ repeat in a cycle of 4: $i, -1, -i, 1$.

Answer 1

The Correct Option is D

Step 1: Recall powers of $i$.
\[ i^1 = i,\quad i^2 = -1,\quad i^3 = -i,\quad i^4 = 1 \]
Step 2: Use cyclic nature.
Powers of $i$ repeat every 4 terms.
Step 3: Reduce the exponent.
\[ 99 \div 4 = 24 \text{ remainder } 3 \]
Step 4: Find the value.
\[ i^{99} = i^3 = -i \]