(6 + 2i)(1 − 5i)/(7 + 4i)

asked by guest
on Jan 23, 2025 at 8:49 am



You asked:

Evaluate the expression: \(\frac{\left(6 + 2 i\right) \left(1 - 5 i\right)}{7 + 4 i}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\left(6 + 2 i\right) \left(1 - 5 i\right)}{7 + 4 i} = \frac{\left(1 - 5 i\right) \left(6 + 2 i\right) \left(7 - 4 i\right)}{65} \)

Expanded

\[\frac{\left(6 + 2 i\right) \left(1 - 5 i\right)}{7 + 4 i} = - 4 i\]

Factored

\[\frac{\left(6 + 2 i\right) \left(1 - 5 i\right)}{7 + 4 i} = \left(\frac{2}{65} - \frac{2 i}{13}\right) \left(3 + i\right) \left(7 - 4 i\right)\]

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

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