Question

\(i^{57}+\dfrac{1}{i^{25}}\), when simplified has the value:

• A. \(0\)
• B. \(2i\)
• C. \(2-2i\)
• D. \(2\)

Hint:

Powers of \(i\) repeat every 4.

Answer 1

The Correct Option is A

Step 1: \[ i^{57}=i^{4\cdot14+1}=i \]
Step 2: \[ \frac{1}{i^{25}}=i^{-25}=i^{4(-6)-1}=-i \]
Step 3: \[ i+(-i)=0 \]