Evaluate
-1+i
Real Part
-1
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-9+3i+2\times 7+2\times \left(3i\right)-i\left(8-6i\right)
Multiply 2 times 7+3i.
-9+3i+\left(14+6i\right)-i\left(8-6i\right)
Do the multiplications in 2\times 7+2\times \left(3i\right).
-9+14+\left(3+6\right)i-i\left(8-6i\right)
Combine the real and imaginary parts in -9+3i+14+6i.
5+9i-i\left(8-6i\right)
Do the additions in -9+14+\left(3+6\right)i.
5+9i-\left(8i-6i^{2}\right)
Multiply i times 8-6i.
5+9i-\left(8i-6\left(-1\right)\right)
By definition, i^{2} is -1.
5+9i-\left(6+8i\right)
Do the multiplications in 8i-6\left(-1\right). Reorder the terms.
5-6+\left(9-8\right)i
Subtract 6+8i from 5+9i by subtracting corresponding real and imaginary parts.
-1+i
Subtract 6 from 5. Subtract 8 from 9.
Re(-9+3i+2\times 7+2\times \left(3i\right)-i\left(8-6i\right))
Multiply 2 times 7+3i.
Re(-9+3i+\left(14+6i\right)-i\left(8-6i\right))
Do the multiplications in 2\times 7+2\times \left(3i\right).
Re(-9+14+\left(3+6\right)i-i\left(8-6i\right))
Combine the real and imaginary parts in -9+3i+14+6i.
Re(5+9i-i\left(8-6i\right))
Do the additions in -9+14+\left(3+6\right)i.
Re(5+9i-\left(8i-6i^{2}\right))
Multiply i times 8-6i.
Re(5+9i-\left(8i-6\left(-1\right)\right))
By definition, i^{2} is -1.
Re(5+9i-\left(6+8i\right))
Do the multiplications in 8i-6\left(-1\right). Reorder the terms.
Re(5-6+\left(9-8\right)i)
Subtract 6+8i from 5+9i by subtracting corresponding real and imaginary parts.
Re(-1+i)
Subtract 6 from 5. Subtract 8 from 9.
-1
The real part of -1+i is -1.
Examples
Quadratic equation
{ 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}