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