Question

divide and simplify to the form ( a + bi ).
( \frac{4i}{1 + i} )
( \frac{4i}{1 + i} = square )
(simplify your answer. use integers or fractions for any numbers in the expression. type your answer in the form

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $1-i$:
$\frac{4i}{1+i} \times \frac{1-i}{1-i} = \frac{4i(1-i)}{(1+i)(1-i)}$

Step2: Expand numerator and denominator

Calculate products:
Numerator: $4i(1-i) = 4i - 4i^2$
Denominator: $(1+i)(1-i) = 1 - i^2$

Step3: Substitute $i^2=-1$

Simplify using $i^2=-1$:
Numerator: $4i - 4(-1) = 4i + 4$
Denominator: $1 - (-1) = 2$

Step4: Split and simplify fraction

Separate terms and divide:
$\frac{4 + 4i}{2} = \frac{4}{2} + \frac{4i}{2} = 2 + 2i$

Answer:

$2 + 2i$