(9-2i)/(2(9+2i))
You asked:
Evaluate the expression: \(\frac{9 - 2 i}{2 \cdot \left(9 + 2 i\right)}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{9 - 2 i}{2 \cdot \left(9 + 2 i\right)} = \frac{\left(9 - 2 i\right) \left(18 - 4 i\right)}{340} \)
Expanded
\[\frac{9 - 2 i}{2 \cdot \left(9 + 2 i\right)} = \frac{77}{170} - \frac{18 i}{85}\]
Factored
\[\frac{9 - 2 i}{2 \cdot \left(9 + 2 i\right)} = \left(\frac{9}{340} - \frac{i}{170}\right) \left(18 - 4 i\right)\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).