$\frac{(4+3i)}{(3-i)}$* $\frac{(3+i)}{(3-i)}$
You asked:
Evaluate the expression: \(\frac{4 + 3 i}{3 - i} \cdot \frac{3 + i}{3 - i}\)
MathBot Answer:
Evaluated
\(\displaystyle \frac{4 + 3 i}{3 - i} \cdot \frac{3 + i}{3 - i} = \frac{\left(3 + i\right)^{3} \cdot \left(4 + 3 i\right)}{100} \)
Expanded
\[\frac{4 + 3 i}{3 - i} \cdot \frac{3 + i}{3 - i} = - \frac{3}{50} + \frac{79 i}{50}\]
Factored
\[\frac{4 + 3 i}{3 - i} \cdot \frac{3 + i}{3 - i} = \left(\frac{1}{25} + \frac{3 i}{100}\right) \left(3 + i\right)^{3}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).