Evaluate
\frac{1}{10}-\frac{1}{10}i=0.1-0.1i
Real Part
\frac{1}{10} = 0.1
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\frac{\left(50+50i\right)i}{500i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(50+50i\right)i}{-500}
By definition, i^{2} is -1. Calculate the denominator.
\frac{50i+50i^{2}}{-500}
Multiply 50+50i times i.
\frac{50i+50\left(-1\right)}{-500}
By definition, i^{2} is -1.
\frac{-50+50i}{-500}
Do the multiplications in 50i+50\left(-1\right). Reorder the terms.
\frac{1}{10}-\frac{1}{10}i
Divide -50+50i by -500 to get \frac{1}{10}-\frac{1}{10}i.
Re(\frac{\left(50+50i\right)i}{500i^{2}})
Multiply both numerator and denominator of \frac{50+50i}{500i} by imaginary unit i.
Re(\frac{\left(50+50i\right)i}{-500})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{50i+50i^{2}}{-500})
Multiply 50+50i times i.
Re(\frac{50i+50\left(-1\right)}{-500})
By definition, i^{2} is -1.
Re(\frac{-50+50i}{-500})
Do the multiplications in 50i+50\left(-1\right). Reorder the terms.
Re(\frac{1}{10}-\frac{1}{10}i)
Divide -50+50i by -500 to get \frac{1}{10}-\frac{1}{10}i.
\frac{1}{10}
The real part of \frac{1}{10}-\frac{1}{10}i is \frac{1}{10}.
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