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