(- \frac{ 3 }{ 5 } + \frac{ 4i }{ 5 } )(- \frac{ 3 }{ 5 } + \frac{ 4 \sqrt{ -1 } }{ 5 }
Evaluate
-\frac{7}{25}-\frac{24}{25}i=-0.28-0.96i
Real Part
-\frac{7}{25} = -0.28
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\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{3}{5}+\frac{4\sqrt{-1}}{5}\right)
Divide 4i by 5 to get \frac{4}{5}i.
\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{3}{5}+\frac{4i}{5}\right)
Calculate the square root of -1 and get i.
\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{3}{5}+\frac{4}{5}i\right)
Divide 4i by 5 to get \frac{4}{5}i.
-\frac{3}{5}\left(-\frac{3}{5}\right)-\frac{3}{5}\times \left(\frac{4}{5}i\right)+\frac{4}{5}i\left(-\frac{3}{5}\right)+\frac{4}{5}\times \frac{4}{5}i^{2}
Multiply complex numbers -\frac{3}{5}+\frac{4}{5}i and -\frac{3}{5}+\frac{4}{5}i like you multiply binomials.
-\frac{3}{5}\left(-\frac{3}{5}\right)-\frac{3}{5}\times \left(\frac{4}{5}i\right)+\frac{4}{5}i\left(-\frac{3}{5}\right)+\frac{4}{5}\times \frac{4}{5}\left(-1\right)
By definition, i^{2} is -1.
\frac{9}{25}-\frac{12}{25}i-\frac{12}{25}i-\frac{16}{25}
Do the multiplications.
\frac{9}{25}-\frac{16}{25}+\left(-\frac{12}{25}-\frac{12}{25}\right)i
Combine the real and imaginary parts.
-\frac{7}{25}-\frac{24}{25}i
Do the additions.
Re(\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{3}{5}+\frac{4\sqrt{-1}}{5}\right))
Divide 4i by 5 to get \frac{4}{5}i.
Re(\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{3}{5}+\frac{4i}{5}\right))
Calculate the square root of -1 and get i.
Re(\left(-\frac{3}{5}+\frac{4}{5}i\right)\left(-\frac{3}{5}+\frac{4}{5}i\right))
Divide 4i by 5 to get \frac{4}{5}i.
Re(-\frac{3}{5}\left(-\frac{3}{5}\right)-\frac{3}{5}\times \left(\frac{4}{5}i\right)+\frac{4}{5}i\left(-\frac{3}{5}\right)+\frac{4}{5}\times \frac{4}{5}i^{2})
Multiply complex numbers -\frac{3}{5}+\frac{4}{5}i and -\frac{3}{5}+\frac{4}{5}i like you multiply binomials.
Re(-\frac{3}{5}\left(-\frac{3}{5}\right)-\frac{3}{5}\times \left(\frac{4}{5}i\right)+\frac{4}{5}i\left(-\frac{3}{5}\right)+\frac{4}{5}\times \frac{4}{5}\left(-1\right))
By definition, i^{2} is -1.
Re(\frac{9}{25}-\frac{12}{25}i-\frac{12}{25}i-\frac{16}{25})
Do the multiplications in -\frac{3}{5}\left(-\frac{3}{5}\right)-\frac{3}{5}\times \left(\frac{4}{5}i\right)+\frac{4}{5}i\left(-\frac{3}{5}\right)+\frac{4}{5}\times \frac{4}{5}\left(-1\right).
Re(\frac{9}{25}-\frac{16}{25}+\left(-\frac{12}{25}-\frac{12}{25}\right)i)
Combine the real and imaginary parts in \frac{9}{25}-\frac{12}{25}i-\frac{12}{25}i-\frac{16}{25}.
Re(-\frac{7}{25}-\frac{24}{25}i)
Do the additions in \frac{9}{25}-\frac{16}{25}+\left(-\frac{12}{25}-\frac{12}{25}\right)i.
-\frac{7}{25}
The real part of -\frac{7}{25}-\frac{24}{25}i is -\frac{7}{25}.
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Integration
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Limits
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