(1+2/i)(3+4/i)(5+i)-1

asked by guest
on Nov 24, 2024 at 9:23 am



You asked:

Evaluate the expression: \(\left(1 + \frac{2}{i}\right) \cdot \left(3 + \frac{4}{i}\right) \cdot \left(5 + i\right) - 1\)

MathBot Answer:

Evaluated



\(\displaystyle \left(1 + \frac{2}{i}\right) \cdot \left(3 + \frac{4}{i}\right) \cdot \left(5 + i\right) - 1 = -1 + \left(1 - 2 i\right) \left(3 - 4 i\right) \left(5 + i\right) \)

Expanded

\[\left(1 + \frac{2}{i}\right) \cdot \left(3 + \frac{4}{i}\right) \cdot \left(5 + i\right) - 1 = -16 - 55 i\]

Factored

\[\left(1 + \frac{2}{i}\right) \cdot \left(3 + \frac{4}{i}\right) \cdot \left(5 + i\right) - 1 = -16 - 55 i\]

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

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