Evaluate
-\frac{3}{5}=-0.6
Real Part
-\frac{3}{5} = -0.6
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\frac{1\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}+\frac{2i}{1-2i}
Multiply both numerator and denominator of \frac{1}{1+2i} by the complex conjugate of the denominator, 1-2i.
\frac{1-2i}{5}+\frac{2i}{1-2i}
Do the multiplications in \frac{1\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}.
\frac{1}{5}-\frac{2}{5}i+\frac{2i}{1-2i}
Divide 1-2i by 5 to get \frac{1}{5}-\frac{2}{5}i.
\frac{1}{5}-\frac{2}{5}i+\frac{2i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}
Multiply both numerator and denominator of \frac{2i}{1-2i} by the complex conjugate of the denominator, 1+2i.
\frac{1}{5}-\frac{2}{5}i+\frac{-4+2i}{5}
Do the multiplications in \frac{2i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}.
\frac{1}{5}-\frac{2}{5}i+\left(-\frac{4}{5}+\frac{2}{5}i\right)
Divide -4+2i by 5 to get -\frac{4}{5}+\frac{2}{5}i.
-\frac{3}{5}
Add \frac{1}{5}-\frac{2}{5}i and -\frac{4}{5}+\frac{2}{5}i to get -\frac{3}{5}.
Re(\frac{1\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}+\frac{2i}{1-2i})
Multiply both numerator and denominator of \frac{1}{1+2i} by the complex conjugate of the denominator, 1-2i.
Re(\frac{1-2i}{5}+\frac{2i}{1-2i})
Do the multiplications in \frac{1\left(1-2i\right)}{\left(1+2i\right)\left(1-2i\right)}.
Re(\frac{1}{5}-\frac{2}{5}i+\frac{2i}{1-2i})
Divide 1-2i by 5 to get \frac{1}{5}-\frac{2}{5}i.
Re(\frac{1}{5}-\frac{2}{5}i+\frac{2i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)})
Multiply both numerator and denominator of \frac{2i}{1-2i} by the complex conjugate of the denominator, 1+2i.
Re(\frac{1}{5}-\frac{2}{5}i+\frac{-4+2i}{5})
Do the multiplications in \frac{2i\left(1+2i\right)}{\left(1-2i\right)\left(1+2i\right)}.
Re(\frac{1}{5}-\frac{2}{5}i+\left(-\frac{4}{5}+\frac{2}{5}i\right))
Divide -4+2i by 5 to get -\frac{4}{5}+\frac{2}{5}i.
Re(-\frac{3}{5})
Add \frac{1}{5}-\frac{2}{5}i and -\frac{4}{5}+\frac{2}{5}i to get -\frac{3}{5}.
-\frac{3}{5}
The real part of -\frac{3}{5} is -\frac{3}{5}.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}