(9-2i)/(2(9+2i))

asked by guest
on Oct 25, 2024 at 10:10 pm



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 \(i^2 = -1\).

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