Evaluate
\frac{3}{8}+\frac{5}{4}i=0.375+1.25i
Real Part
\frac{3}{8} = 0.375
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\frac{\left(10-3i\right)i}{-8i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(10-3i\right)i}{8}
By definition, i^{2} is -1. Calculate the denominator.
\frac{10i-3i^{2}}{8}
Multiply 10-3i times i.
\frac{10i-3\left(-1\right)}{8}
By definition, i^{2} is -1.
\frac{3+10i}{8}
Do the multiplications in 10i-3\left(-1\right). Reorder the terms.
\frac{3}{8}+\frac{5}{4}i
Divide 3+10i by 8 to get \frac{3}{8}+\frac{5}{4}i.
Re(\frac{\left(10-3i\right)i}{-8i^{2}})
Multiply both numerator and denominator of \frac{10-3i}{-8i} by imaginary unit i.
Re(\frac{\left(10-3i\right)i}{8})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{10i-3i^{2}}{8})
Multiply 10-3i times i.
Re(\frac{10i-3\left(-1\right)}{8})
By definition, i^{2} is -1.
Re(\frac{3+10i}{8})
Do the multiplications in 10i-3\left(-1\right). Reorder the terms.
Re(\frac{3}{8}+\frac{5}{4}i)
Divide 3+10i by 8 to get \frac{3}{8}+\frac{5}{4}i.
\frac{3}{8}
The real part of \frac{3}{8}+\frac{5}{4}i is \frac{3}{8}.
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