Evaluate
-19+14i
Real Part
-19
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5\left(-2\right)+5\times \left(4i\right)-3\left(3+2i\right)
Multiply 5 times -2+4i.
-10+20i-3\left(3+2i\right)
Do the multiplications in 5\left(-2\right)+5\times \left(4i\right).
-10+20i-\left(3\times 3+3\times \left(2i\right)\right)
Multiply 3 times 3+2i.
-10+20i-\left(9+6i\right)
Do the multiplications in 3\times 3+3\times \left(2i\right).
-10-9+\left(20-6\right)i
Subtract 9+6i from -10+20i by subtracting corresponding real and imaginary parts.
-19+14i
Subtract 9 from -10. Subtract 6 from 20.
Re(5\left(-2\right)+5\times \left(4i\right)-3\left(3+2i\right))
Multiply 5 times -2+4i.
Re(-10+20i-3\left(3+2i\right))
Do the multiplications in 5\left(-2\right)+5\times \left(4i\right).
Re(-10+20i-\left(3\times 3+3\times \left(2i\right)\right))
Multiply 3 times 3+2i.
Re(-10+20i-\left(9+6i\right))
Do the multiplications in 3\times 3+3\times \left(2i\right).
Re(-10-9+\left(20-6\right)i)
Subtract 9+6i from -10+20i by subtracting corresponding real and imaginary parts.
Re(-19+14i)
Subtract 9 from -10. Subtract 6 from 20.
-19
The real part of -19+14i is -19.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
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y = 3x + 4
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\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}