Evaluate
5-38i
Real Part
5
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7\times 3+7\times \left(-2i\right)-8i\times 3-8\left(-2\right)i^{2}
Multiply complex numbers 7-8i and 3-2i like you multiply binomials.
7\times 3+7\times \left(-2i\right)-8i\times 3-8\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
21-14i-24i-16
Do the multiplications.
21-16+\left(-14-24\right)i
Combine the real and imaginary parts.
5-38i
Do the additions.
Re(7\times 3+7\times \left(-2i\right)-8i\times 3-8\left(-2\right)i^{2})
Multiply complex numbers 7-8i and 3-2i like you multiply binomials.
Re(7\times 3+7\times \left(-2i\right)-8i\times 3-8\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(21-14i-24i-16)
Do the multiplications in 7\times 3+7\times \left(-2i\right)-8i\times 3-8\left(-2\right)\left(-1\right).
Re(21-16+\left(-14-24\right)i)
Combine the real and imaginary parts in 21-14i-24i-16.
Re(5-38i)
Do the additions in 21-16+\left(-14-24\right)i.
5
The real part of 5-38i is 5.
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{ x } ^ { 2 } - 4 x - 5 = 0
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4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
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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}