Evaluate
-3+3i
Real Part
-3
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3i\left(1+i\right)
Calculate the square root of 2i and get 1+i.
3i\times 1+3i^{2}
Multiply 3i times 1+i.
3i\times 1+3\left(-1\right)
By definition, i^{2} is -1.
-3+3i
Do the multiplications. Reorder the terms.
Re(3i\left(1+i\right))
Calculate the square root of 2i and get 1+i.
Re(3i\times 1+3i^{2})
Multiply 3i times 1+i.
Re(3i\times 1+3\left(-1\right))
By definition, i^{2} is -1.
Re(-3+3i)
Do the multiplications in 3i\times 1+3\left(-1\right). Reorder the terms.
-3
The real part of -3+3i 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}