((21/5*i)(-7/2-3/4*i))/((3/4*i-7/2)(-7/2-3/4*i))

asked by guest
on Nov 23, 2024 at 3:54 am



You asked:

Evaluate the expression: \(\frac{\frac{21}{5} \cdot i \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\frac{21}{5} \cdot i \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)} = \frac{5376 i \left(- \frac{7}{2} - \frac{3 i}{4}\right)^{2} \left(- \frac{7}{2} + \frac{3 i}{4}\right)}{210125} \)

Expanded

\[\frac{\frac{21}{5} \cdot i \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)} = \frac{252}{1025} - \frac{1176 i}{1025}\]

Factored

\[\frac{\frac{21}{5} \cdot i \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)} = \frac{84 i \left(-14 - 3 i\right)^{2} \left(-14 + 3 i\right)}{210125}\]

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

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