Evaluate
\frac{29}{4}-2i=7.25-2i
Real Part
\frac{29}{4} = 7\frac{1}{4} = 7.25
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-\left(\frac{3}{4}+\frac{3}{2}\left(-i\right)\right)-\left(-7-i^{12}\right)+\frac{7}{2}i^{27}
Calculate i to the power of 35 and get -i.
-\frac{3}{4}+\frac{3}{2}i-\left(-7-i^{12}\right)+\frac{7}{2}i^{27}
Multiply \frac{3}{2} and -i to get -\frac{3}{2}i.
-\frac{3}{4}+\frac{3}{2}i-\left(-7-1\right)+\frac{7}{2}i^{27}
Calculate i to the power of 12 and get 1.
-\frac{3}{4}+\frac{3}{2}i-\left(-8\right)+\frac{7}{2}i^{27}
Subtract 1 from -7 to get -8.
-\frac{3}{4}+\frac{3}{2}i+8+\frac{7}{2}i^{27}
The opposite of -8 is 8.
\frac{29}{4}+\frac{3}{2}i+\frac{7}{2}i^{27}
Add -\frac{3}{4}+\frac{3}{2}i and 8 to get \frac{29}{4}+\frac{3}{2}i.
\frac{29}{4}+\frac{3}{2}i+\frac{7}{2}\left(-i\right)
Calculate i to the power of 27 and get -i.
\frac{29}{4}+\frac{3}{2}i-\frac{7}{2}i
Multiply \frac{7}{2} and -i to get -\frac{7}{2}i.
\frac{29}{4}-2i
Subtract \frac{7}{2}i from \frac{29}{4}+\frac{3}{2}i to get \frac{29}{4}-2i.
Re(-\left(\frac{3}{4}+\frac{3}{2}\left(-i\right)\right)-\left(-7-i^{12}\right)+\frac{7}{2}i^{27})
Calculate i to the power of 35 and get -i.
Re(-\frac{3}{4}+\frac{3}{2}i-\left(-7-i^{12}\right)+\frac{7}{2}i^{27})
Multiply \frac{3}{2} and -i to get -\frac{3}{2}i.
Re(-\frac{3}{4}+\frac{3}{2}i-\left(-7-1\right)+\frac{7}{2}i^{27})
Calculate i to the power of 12 and get 1.
Re(-\frac{3}{4}+\frac{3}{2}i-\left(-8\right)+\frac{7}{2}i^{27})
Subtract 1 from -7 to get -8.
Re(-\frac{3}{4}+\frac{3}{2}i+8+\frac{7}{2}i^{27})
The opposite of -8 is 8.
Re(\frac{29}{4}+\frac{3}{2}i+\frac{7}{2}i^{27})
Add -\frac{3}{4}+\frac{3}{2}i and 8 to get \frac{29}{4}+\frac{3}{2}i.
Re(\frac{29}{4}+\frac{3}{2}i+\frac{7}{2}\left(-i\right))
Calculate i to the power of 27 and get -i.
Re(\frac{29}{4}+\frac{3}{2}i-\frac{7}{2}i)
Multiply \frac{7}{2} and -i to get -\frac{7}{2}i.
Re(\frac{29}{4}-2i)
Subtract \frac{7}{2}i from \frac{29}{4}+\frac{3}{2}i to get \frac{29}{4}-2i.
\frac{29}{4}
The real part of \frac{29}{4}-2i is \frac{29}{4}.
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