Evaluate
-\frac{7}{6}-3i\approx -1.166666667-3i
Real Part
-\frac{7}{6} = -1\frac{1}{6} = -1.1666666666666667
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\frac{\left(18-7i\right)i}{6i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(18-7i\right)i}{-6}
By definition, i^{2} is -1. Calculate the denominator.
\frac{18i-7i^{2}}{-6}
Multiply 18-7i times i.
\frac{18i-7\left(-1\right)}{-6}
By definition, i^{2} is -1.
\frac{7+18i}{-6}
Do the multiplications in 18i-7\left(-1\right). Reorder the terms.
-\frac{7}{6}-3i
Divide 7+18i by -6 to get -\frac{7}{6}-3i.
Re(\frac{\left(18-7i\right)i}{6i^{2}})
Multiply both numerator and denominator of \frac{18-7i}{6i} by imaginary unit i.
Re(\frac{\left(18-7i\right)i}{-6})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{18i-7i^{2}}{-6})
Multiply 18-7i times i.
Re(\frac{18i-7\left(-1\right)}{-6})
By definition, i^{2} is -1.
Re(\frac{7+18i}{-6})
Do the multiplications in 18i-7\left(-1\right). Reorder the terms.
Re(-\frac{7}{6}-3i)
Divide 7+18i by -6 to get -\frac{7}{6}-3i.
-\frac{7}{6}
The real part of -\frac{7}{6}-3i is -\frac{7}{6}.
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