Evaluate
\frac{1}{2}-\frac{5}{4}i=0.5-1.25i
Real Part
\frac{1}{2} = 0.5
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\frac{\left(5+2i\right)i}{4i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(5+2i\right)i}{-4}
By definition, i^{2} is -1. Calculate the denominator.
\frac{5i+2i^{2}}{-4}
Multiply 5+2i times i.
\frac{5i+2\left(-1\right)}{-4}
By definition, i^{2} is -1.
\frac{-2+5i}{-4}
Do the multiplications in 5i+2\left(-1\right). Reorder the terms.
\frac{1}{2}-\frac{5}{4}i
Divide -2+5i by -4 to get \frac{1}{2}-\frac{5}{4}i.
Re(\frac{\left(5+2i\right)i}{4i^{2}})
Multiply both numerator and denominator of \frac{5+2i}{4i} by imaginary unit i.
Re(\frac{\left(5+2i\right)i}{-4})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{5i+2i^{2}}{-4})
Multiply 5+2i times i.
Re(\frac{5i+2\left(-1\right)}{-4})
By definition, i^{2} is -1.
Re(\frac{-2+5i}{-4})
Do the multiplications in 5i+2\left(-1\right). Reorder the terms.
Re(\frac{1}{2}-\frac{5}{4}i)
Divide -2+5i by -4 to get \frac{1}{2}-\frac{5}{4}i.
\frac{1}{2}
The real part of \frac{1}{2}-\frac{5}{4}i is \frac{1}{2}.
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