Evaluate
6-54i
Real Part
6
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5\times 6+5\times \left(-6i\right)-4i\times 6-4\left(-6\right)i^{2}
Multiply complex numbers 5-4i and 6-6i like you multiply binomials.
5\times 6+5\times \left(-6i\right)-4i\times 6-4\left(-6\right)\left(-1\right)
By definition, i^{2} is -1.
30-30i-24i-24
Do the multiplications.
30-24+\left(-30-24\right)i
Combine the real and imaginary parts.
6-54i
Do the additions.
Re(5\times 6+5\times \left(-6i\right)-4i\times 6-4\left(-6\right)i^{2})
Multiply complex numbers 5-4i and 6-6i like you multiply binomials.
Re(5\times 6+5\times \left(-6i\right)-4i\times 6-4\left(-6\right)\left(-1\right))
By definition, i^{2} is -1.
Re(30-30i-24i-24)
Do the multiplications in 5\times 6+5\times \left(-6i\right)-4i\times 6-4\left(-6\right)\left(-1\right).
Re(30-24+\left(-30-24\right)i)
Combine the real and imaginary parts in 30-30i-24i-24.
Re(6-54i)
Do the additions in 30-24+\left(-30-24\right)i.
6
The real part of 6-54i is 6.
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{ x } ^ { 2 } - 4 x - 5 = 0
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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}