Question

divide.
\\(\frac{5i}{1 - i}\\)
write your answer as a complex number in standard form.

Explanation:

Step1: Multiply by conjugate of denominator

Multiply numerator and denominator by $1+i$:
$$\frac{5i}{1-i} \times \frac{1+i}{1+i} = \frac{5i(1+i)}{(1-i)(1+i)}$$

Step2: Expand numerator and denominator

Calculate products using $i^2=-1$:
$$\frac{5i + 5i^2}{1^2 - i^2} = \frac{5i + 5(-1)}{1 - (-1)}$$

Step3: Simplify numerator and denominator

Combine like terms and constants:
$$\frac{-5 + 5i}{2} = -\frac{5}{2} + \frac{5}{2}i$$

Answer:

$-\frac{5}{2} + \frac{5}{2}i$