Evaluate
5-5i
Real Part
5
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\frac{5\times \left(-5i\right)+5\left(-5\right)i^{2}}{5}
Multiply 5+5i times -5i.
\frac{5\times \left(-5i\right)+5\left(-5\right)\left(-1\right)}{5}
By definition, i^{2} is -1.
\frac{25-25i}{5}
Do the multiplications in 5\times \left(-5i\right)+5\left(-5\right)\left(-1\right). Reorder the terms.
5-5i
Divide 25-25i by 5 to get 5-5i.
Re(\frac{5\times \left(-5i\right)+5\left(-5\right)i^{2}}{5})
Multiply 5+5i times -5i.
Re(\frac{5\times \left(-5i\right)+5\left(-5\right)\left(-1\right)}{5})
By definition, i^{2} is -1.
Re(\frac{25-25i}{5})
Do the multiplications in 5\times \left(-5i\right)+5\left(-5\right)\left(-1\right). Reorder the terms.
Re(5-5i)
Divide 25-25i by 5 to get 5-5i.
5
The real part of 5-5i is 5.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}