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

asked by guest
on Nov 23, 2024 at 3:09 am



You asked:

Evaluate the expression: \(\frac{\left(i + 2\right) \cdot \left(i + 2\right)}{\left(2 - i\right) \cdot \left(2 + i\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\left(i + 2\right) \cdot \left(i + 2\right)}{\left(2 - i\right) \cdot \left(2 + i\right)} = \frac{\left(2 - i\right) \left(2 + i\right)^{3}}{25} \)

Expanded

\[\frac{\left(i + 2\right) \cdot \left(i + 2\right)}{\left(2 - i\right) \cdot \left(2 + i\right)} = \frac{3}{5} + \frac{4 i}{5}\]

Factored

\[\frac{\left(i + 2\right) \cdot \left(i + 2\right)}{\left(2 - i\right) \cdot \left(2 + i\right)} = \left(\frac{2}{25} - \frac{i}{25}\right) \left(2 + i\right)^{3}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

+ Submit Question