Evaluate
3-5i
Real Part
3
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\frac{\left(5+3i\right)i}{1i^{2}}
Multiply both numerator and denominator by imaginary unit i.
\frac{\left(5+3i\right)i}{-1}
By definition, i^{2} is -1. Calculate the denominator.
\frac{5i+3i^{2}}{-1}
Multiply 5+3i times i.
\frac{5i+3\left(-1\right)}{-1}
By definition, i^{2} is -1.
\frac{-3+5i}{-1}
Do the multiplications in 5i+3\left(-1\right). Reorder the terms.
3-5i
Divide -3+5i by -1 to get 3-5i.
Re(\frac{\left(5+3i\right)i}{1i^{2}})
Multiply both numerator and denominator of \frac{5+3i}{i} by imaginary unit i.
Re(\frac{\left(5+3i\right)i}{-1})
By definition, i^{2} is -1. Calculate the denominator.
Re(\frac{5i+3i^{2}}{-1})
Multiply 5+3i times i.
Re(\frac{5i+3\left(-1\right)}{-1})
By definition, i^{2} is -1.
Re(\frac{-3+5i}{-1})
Do the multiplications in 5i+3\left(-1\right). Reorder the terms.
Re(3-5i)
Divide -3+5i by -1 to get 3-5i.
3
The real part of 3-5i is 3.
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}