Question

watch the video and then solve the problem given below. click here to watch the video. divide and simplify to the form ( a + bi ). ( \frac{8i}{1 + i} ) ( \frac{8i}{1 + i} = square ) (simplify your answer. use integers or fractions for any numbers in the expression. type your answer in the form ( a + bi ).)

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $1-i$ (the conjugate of $1+i$):
$\frac{8i}{1+i} \times \frac{1-i}{1-i} = \frac{8i(1-i)}{(1+i)(1-i)}$

Step2: Expand numerator and denominator

Expand using distributive property and $i^2=-1$:
Numerator: $8i(1-i) = 8i - 8i^2 = 8i - 8(-1) = 8 + 8i$
Denominator: $(1+i)(1-i) = 1^2 - i^2 = 1 - (-1) = 2$
Expression becomes: $\frac{8 + 8i}{2}$

Step3: Split and simplify fraction

Divide each term in numerator by denominator:
$\frac{8}{2} + \frac{8i}{2} = 4 + 4i$

Answer:

$4 + 4i$