Evaluate
9+38i
Real Part
9
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-3\times 5-3\times \left(-6i\right)+4i\times 5+4\left(-6\right)i^{2}
Multiply complex numbers -3+4i and 5-6i like you multiply binomials.
-3\times 5-3\times \left(-6i\right)+4i\times 5+4\left(-6\right)\left(-1\right)
By definition, i^{2} is -1.
-15+18i+20i+24
Do the multiplications.
-15+24+\left(18+20\right)i
Combine the real and imaginary parts.
9+38i
Do the additions.
Re(-3\times 5-3\times \left(-6i\right)+4i\times 5+4\left(-6\right)i^{2})
Multiply complex numbers -3+4i and 5-6i like you multiply binomials.
Re(-3\times 5-3\times \left(-6i\right)+4i\times 5+4\left(-6\right)\left(-1\right))
By definition, i^{2} is -1.
Re(-15+18i+20i+24)
Do the multiplications in -3\times 5-3\times \left(-6i\right)+4i\times 5+4\left(-6\right)\left(-1\right).
Re(-15+24+\left(18+20\right)i)
Combine the real and imaginary parts in -15+18i+20i+24.
Re(9+38i)
Do the additions in -15+24+\left(18+20\right)i.
9
The real part of 9+38i is 9.
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{ x } ^ { 2 } - 4 x - 5 = 0
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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
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