Evaluate
-22+7i
Real Part
-22
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-2\times 5-2\times \left(4i\right)+3i\times 5+3\times 4i^{2}
Multiply complex numbers -2+3i and 5+4i like you multiply binomials.
-2\times 5-2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right)
By definition, i^{2} is -1.
-10-8i+15i-12
Do the multiplications.
-10-12+\left(-8+15\right)i
Combine the real and imaginary parts.
-22+7i
Do the additions.
Re(-2\times 5-2\times \left(4i\right)+3i\times 5+3\times 4i^{2})
Multiply complex numbers -2+3i and 5+4i like you multiply binomials.
Re(-2\times 5-2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right))
By definition, i^{2} is -1.
Re(-10-8i+15i-12)
Do the multiplications in -2\times 5-2\times \left(4i\right)+3i\times 5+3\times 4\left(-1\right).
Re(-10-12+\left(-8+15\right)i)
Combine the real and imaginary parts in -10-8i+15i-12.
Re(-22+7i)
Do the additions in -10-12+\left(-8+15\right)i.
-22
The real part of -22+7i is -22.
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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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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}