Evaluate
\frac{5}{3}+\frac{2}{3}i\approx 1.666666667+0.666666667i
Real Part
\frac{5}{3} = 1\frac{2}{3} = 1.6666666666666667
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\left(\frac{2}{3}-\frac{5}{3}i\right)i
Divide 2-5i by 3 to get \frac{2}{3}-\frac{5}{3}i.
\frac{2}{3}i-\frac{5}{3}i^{2}
Multiply \frac{2}{3}-\frac{5}{3}i times i.
\frac{2}{3}i-\frac{5}{3}\left(-1\right)
By definition, i^{2} is -1.
\frac{5}{3}+\frac{2}{3}i
Do the multiplications. Reorder the terms.
Re(\left(\frac{2}{3}-\frac{5}{3}i\right)i)
Divide 2-5i by 3 to get \frac{2}{3}-\frac{5}{3}i.
Re(\frac{2}{3}i-\frac{5}{3}i^{2})
Multiply \frac{2}{3}-\frac{5}{3}i times i.
Re(\frac{2}{3}i-\frac{5}{3}\left(-1\right))
By definition, i^{2} is -1.
Re(\frac{5}{3}+\frac{2}{3}i)
Do the multiplications in \frac{2}{3}i-\frac{5}{3}\left(-1\right). Reorder the terms.
\frac{5}{3}
The real part of \frac{5}{3}+\frac{2}{3}i is \frac{5}{3}.
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