Evaluate
\frac{3}{2}+\frac{9}{4}i=1.5+2.25i
Real Part
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\frac{\left(9-6i\right)i}{-4i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(9-6i\right)i}{4}
By definition, i^{2} is -1. Calculate the denominator.
\frac{9i-6i^{2}}{4}
Multiply 9-6i times i.
\frac{9i-6\left(-1\right)}{4}
By definition, i^{2} is -1.
\frac{6+9i}{4}
Do the multiplications in 9i-6\left(-1\right). Reorder the terms.
\frac{3}{2}+\frac{9}{4}i
Divide 6+9i by 4 to get \frac{3}{2}+\frac{9}{4}i.
Re(\frac{\left(9-6i\right)i}{-4i^{2}})
Multiply both numerator and denominator of \frac{9-6i}{-4i} by imaginary unit i.
Re(\frac{\left(9-6i\right)i}{4})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{9i-6i^{2}}{4})
Multiply 9-6i times i.
Re(\frac{9i-6\left(-1\right)}{4})
By definition, i^{2} is -1.
Re(\frac{6+9i}{4})
Do the multiplications in 9i-6\left(-1\right). Reorder the terms.
Re(\frac{3}{2}+\frac{9}{4}i)
Divide 6+9i by 4 to get \frac{3}{2}+\frac{9}{4}i.
\frac{3}{2}
The real part of \frac{3}{2}+\frac{9}{4}i is \frac{3}{2}.
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Limits
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