(3+3(2)^1/2i)/(2+2i)
You asked:
Evaluate the expression: \(\frac{3 + \frac{3 \cdot {2}^{1}}{2 i}}{2 + 2 i}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{3 + \frac{3 \cdot {2}^{1}}{2 i}}{2 + 2 i} = \frac{\left(2 - 2 i\right) \left(3 - 3 i\right)}{8} \)
Expanded
\[\frac{3 + \frac{3 \cdot {2}^{1}}{2 i}}{2 + 2 i} = - \frac{3 i}{2}\]
Factored
\[\frac{3 + \frac{3 \cdot {2}^{1}}{2 i}}{2 + 2 i} = \left(\frac{1}{4} - \frac{i}{4}\right) \left(3 - 3 i\right)\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).