Evaluate (complex solution)
16-4i
Real Part (complex solution)
16
Evaluate
\text{Indeterminate}
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\left(5+3i\right)\left(2-\sqrt{-4}\right)
Calculate the square root of -9 and get 3i.
\left(5+3i\right)\left(2-2i\right)
Calculate the square root of -4 and get 2i.
5\times 2+5\times \left(-2i\right)+3i\times 2+3\left(-2\right)i^{2}
Multiply complex numbers 5+3i and 2-2i like you multiply binomials.
5\times 2+5\times \left(-2i\right)+3i\times 2+3\left(-2\right)\left(-1\right)
By definition, i^{2} is -1.
10-10i+6i+6
Do the multiplications.
10+6+\left(-10+6\right)i
Combine the real and imaginary parts.
16-4i
Do the additions.
Re(\left(5+3i\right)\left(2-\sqrt{-4}\right))
Calculate the square root of -9 and get 3i.
Re(\left(5+3i\right)\left(2-2i\right))
Calculate the square root of -4 and get 2i.
Re(5\times 2+5\times \left(-2i\right)+3i\times 2+3\left(-2\right)i^{2})
Multiply complex numbers 5+3i and 2-2i like you multiply binomials.
Re(5\times 2+5\times \left(-2i\right)+3i\times 2+3\left(-2\right)\left(-1\right))
By definition, i^{2} is -1.
Re(10-10i+6i+6)
Do the multiplications in 5\times 2+5\times \left(-2i\right)+3i\times 2+3\left(-2\right)\left(-1\right).
Re(10+6+\left(-10+6\right)i)
Combine the real and imaginary parts in 10-10i+6i+6.
Re(16-4i)
Do the additions in 10+6+\left(-10+6\right)i.
16
The real part of 16-4i is 16.
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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
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