Question

directions this diagnostic assesses your knowledge of this topic. question 1 simplify $i^{54}$. \\(\circ 1\\) \\(\circ i\\) \\(\circ -1\\) \\(\circ -i\\)

Explanation:

Step1: Find remainder of exponent ÷4

$54 \div 4 = 13$ remainder $2$

Step2: Use $i$ cycle property

$i^{54}=i^{4\times13 + 2}=(i^4)^{13}\times i^2$
Since $i^4=1$, this simplifies to $1^{13}\times i^2 = i^2$

Step3: Substitute $i^2=-1$

$i^2=-1$

Answer:

-1