Question

question 4 (4 points) simplify. upload your handwritten work displaying how you solved to receive credit. 22.29

Explanation:

Step1: Recall $i$ cycle pattern

$i^1=i$, $i^2=-1$, $i^3=-i$, $i^4=1$; cycle repeats every 4.

Step2: Divide exponent by 4

$29 \div 4 = 7$ remainder $1$, so $i^{29}=i^{4\times7 + 1}=(i^4)^7 \times i^1$

Step3: Substitute $i^4=1$

$(1)^7 \times i = 1 \times i = i$

Step4: Multiply by coefficient 2

$2 \times i = 2i$

Answer:

$2i$