Question

question
evaluate:
$i^{11} \cdot i^{28} \cdot i^{26} \cdot i^{20}$
answer
$\bigcirc \\ i$
$\bigcirc \\ -i$
$\bigcirc \\ 1$
$\bigcirc \\ -1$

Explanation:

Step1: Add exponents of $i$

$i^{11+28+26+20} = i^{85}$

Step2: Divide exponent by 4, find remainder

$85 \div 4 = 21$ remainder $1$, so $i^{85}=i^{4\times21 + 1}=(i^4)^{21}\cdot i^1$

Step3: Simplify using $i^4=1$

$(1)^{21}\cdot i = 1\cdot i = i$

Answer:

$i$