Question

question
evaluate:
$i^{43} \cdot i^{49}$
answer
$\bigcirc \\ i$
$\bigcirc \\ -i$
$\bigcirc \\ -1$
$\bigcirc \\ 1$

Explanation:

Step1: Add exponents of $i$

$i^{43} \cdot i^{49} = i^{43+49} = i^{92}$

Step2: Divide exponent by 4

$92 \div 4 = 23$, remainder = 0

Step3: Use $i^4=1$ rule

Since remainder is 0, $i^{92}=(i^4)^{23}=1^{23}$

Step4: Simplify the expression

$1^{23}=1$

Answer:

1