Evaluate
-14+5i
Real Part
-14
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-i-3+\left(-6+3i\right)-\left(5-3i\right)
Multiply -1 and 6-3i to get -6+3i.
-3-6+\left(-1+3\right)i-\left(5-3i\right)
Combine the real and imaginary parts in -i-3+\left(-6+3i\right).
-9+2i-\left(5-3i\right)
Do the additions in -3-6+\left(-1+3\right)i.
-9+2i+\left(-5+3i\right)
Multiply -1 and 5-3i to get -5+3i.
-9-5+\left(2+3\right)i
Combine the real and imaginary parts.
-14+5i
Do the additions.
Re(-i-3+\left(-6+3i\right)-\left(5-3i\right))
Multiply -1 and 6-3i to get -6+3i.
Re(-3-6+\left(-1+3\right)i-\left(5-3i\right))
Combine the real and imaginary parts in -i-3+\left(-6+3i\right).
Re(-9+2i-\left(5-3i\right))
Do the additions in -3-6+\left(-1+3\right)i.
Re(-9+2i+\left(-5+3i\right))
Multiply -1 and 5-3i to get -5+3i.
Re(-9-5+\left(2+3\right)i)
Combine the real and imaginary parts in -9+2i+\left(-5+3i\right).
Re(-14+5i)
Do the additions in -9-5+\left(2+3\right)i.
-14
The real part of -14+5i is -14.
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y = 3x + 4
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Matrix
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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}