Evaluate
1+i
Real Part
1
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\frac{2+2i}{1\times 1+1\left(-i\right)+i-i^{2}}
Multiply complex numbers 1+i and 1-i like you multiply binomials.
\frac{2+2i}{1\times 1+1\left(-i\right)+i-\left(-1\right)}
By definition, i^{2} is -1.
\frac{2+2i}{1-i+i+1}
Do the multiplications in 1\times 1+1\left(-i\right)+i-\left(-1\right).
\frac{2+2i}{1+1+\left(-1+1\right)i}
Combine the real and imaginary parts in 1-i+i+1.
\frac{2+2i}{2}
Do the additions in 1+1+\left(-1+1\right)i.
1+i
Divide 2+2i by 2 to get 1+i.
Re(\frac{2+2i}{1\times 1+1\left(-i\right)+i-i^{2}})
Multiply complex numbers 1+i and 1-i like you multiply binomials.
Re(\frac{2+2i}{1\times 1+1\left(-i\right)+i-\left(-1\right)})
By definition, i^{2} is -1.
Re(\frac{2+2i}{1-i+i+1})
Do the multiplications in 1\times 1+1\left(-i\right)+i-\left(-1\right).
Re(\frac{2+2i}{1+1+\left(-1+1\right)i})
Combine the real and imaginary parts in 1-i+i+1.
Re(\frac{2+2i}{2})
Do the additions in 1+1+\left(-1+1\right)i.
Re(1+i)
Divide 2+2i by 2 to get 1+i.
1
The real part of 1+i is 1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
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Matrix
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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}