Evaluate
\frac{3}{2}+\frac{1}{2}i=1.5+0.5i
Real Part
\frac{3}{2} = 1\frac{1}{2} = 1.5
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\frac{4+2\left(1+i\right)}{4}
Calculate the square root of 2i and get 1+i.
\frac{4+2\times 1+2i}{4}
Multiply 2 times 1+i.
\frac{4+\left(2+2i\right)}{4}
Do the multiplications in 2\times 1+2i.
\frac{4+2+2i}{4}
Combine the real and imaginary parts in 4+2+2i.
\frac{6+2i}{4}
Add 4 to 2.
\frac{3}{2}+\frac{1}{2}i
Divide 6+2i by 4 to get \frac{3}{2}+\frac{1}{2}i.
Re(\frac{4+2\left(1+i\right)}{4})
Calculate the square root of 2i and get 1+i.
Re(\frac{4+2\times 1+2i}{4})
Multiply 2 times 1+i.
Re(\frac{4+\left(2+2i\right)}{4})
Do the multiplications in 2\times 1+2i.
Re(\frac{4+2+2i}{4})
Combine the real and imaginary parts in 4+2+2i.
Re(\frac{6+2i}{4})
Add 4 to 2.
Re(\frac{3}{2}+\frac{1}{2}i)
Divide 6+2i by 4 to get \frac{3}{2}+\frac{1}{2}i.
\frac{3}{2}
The real part of \frac{3}{2}+\frac{1}{2}i is \frac{3}{2}.
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