Evaluate
\frac{1}{2}+\frac{5}{2}i=0.5+2.5i
Real Part
\frac{1}{2} = 0.5
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\frac{\left(-5+i\right)i}{2i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(-5+i\right)i}{-2}
By definition, i^{2} is -1. Calculate the denominator.
\frac{-5i+i^{2}}{-2}
Multiply -5+i times i.
\frac{-5i-1}{-2}
By definition, i^{2} is -1.
\frac{-1-5i}{-2}
Reorder the terms.
\frac{1}{2}+\frac{5}{2}i
Divide -1-5i by -2 to get \frac{1}{2}+\frac{5}{2}i.
Re(\frac{\left(-5+i\right)i}{2i^{2}})
Multiply both numerator and denominator of \frac{-5+i}{2i} by imaginary unit i.
Re(\frac{\left(-5+i\right)i}{-2})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{-5i+i^{2}}{-2})
Multiply -5+i times i.
Re(\frac{-5i-1}{-2})
By definition, i^{2} is -1.
Re(\frac{-1-5i}{-2})
Reorder the terms.
Re(\frac{1}{2}+\frac{5}{2}i)
Divide -1-5i by -2 to get \frac{1}{2}+\frac{5}{2}i.
\frac{1}{2}
The real part of \frac{1}{2}+\frac{5}{2}i is \frac{1}{2}.
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