Evaluate
\frac{1}{2}-\frac{3}{4}i=0.5-0.75i
Real Part
\frac{1}{2} = 0.5
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\frac{\left(4-6i\right)i^{4}}{\left(2-2i\right)\left(2+2i\right)}
Multiply 2-3i and 2 to get 4-6i.
\frac{\left(4-6i\right)\times 1}{\left(2-2i\right)\left(2+2i\right)}
Calculate i to the power of 4 and get 1.
\frac{4-6i}{\left(2-2i\right)\left(2+2i\right)}
Multiply 4-6i and 1 to get 4-6i.
\frac{4-6i}{8}
Multiply 2-2i and 2+2i to get 8.
\frac{1}{2}-\frac{3}{4}i
Divide 4-6i by 8 to get \frac{1}{2}-\frac{3}{4}i.
Re(\frac{\left(4-6i\right)i^{4}}{\left(2-2i\right)\left(2+2i\right)})
Multiply 2-3i and 2 to get 4-6i.
Re(\frac{\left(4-6i\right)\times 1}{\left(2-2i\right)\left(2+2i\right)})
Calculate i to the power of 4 and get 1.
Re(\frac{4-6i}{\left(2-2i\right)\left(2+2i\right)})
Multiply 4-6i and 1 to get 4-6i.
Re(\frac{4-6i}{8})
Multiply 2-2i and 2+2i to get 8.
Re(\frac{1}{2}-\frac{3}{4}i)
Divide 4-6i by 8 to get \frac{1}{2}-\frac{3}{4}i.
\frac{1}{2}
The real part of \frac{1}{2}-\frac{3}{4}i is \frac{1}{2}.
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