((21/5*i+12/5)(-7/2-3/4*i))/((3/4*i-7/2)(-7/2-3/4*i))

asked by guest
on Nov 23, 2024 at 4:30 am



You asked:

Evaluate the expression: \(\frac{\left(\frac{21}{5} \cdot i + \frac{12}{5}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}\)

MathBot Answer:

Evaluated



\(\displaystyle \frac{\left(\frac{21}{5} \cdot i + \frac{12}{5}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)} = \frac{256 \left(- \frac{7}{2} - \frac{3 i}{4}\right)^{2} \left(- \frac{7}{2} + \frac{3 i}{4}\right) \left(\frac{12}{5} + \frac{21 i}{5}\right)}{42025} \)

Expanded

\[\frac{\left(\frac{21}{5} \cdot i + \frac{12}{5}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)} = - \frac{84}{205} - \frac{264 i}{205}\]

Factored

\[\frac{\left(\frac{21}{5} \cdot i + \frac{12}{5}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)}{\left(\frac{3}{4} \cdot i - \frac{7}{2}\right) \cdot \left(\frac{-7}{2} - \frac{3}{4} \cdot i\right)} = \left(-14 - 3 i\right)^{2} \left(- \frac{168}{210125} + \frac{36 i}{210125}\right) \left(4 + 7 i\right)\]

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

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