Solve for x (complex solution)
x\in \mathrm{C}
Solve for y (complex solution)
y\in \mathrm{C}
Solve for x
x\in \mathrm{R}
Solve for y
y\in \mathrm{R}
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0x+0y=0\times 3
Do the multiplications.
0+0y=0\times 3
Anything times zero gives zero.
0+0=0\times 3
Anything times zero gives zero.
0=0\times 3
Add 0 and 0 to get 0.
0=0
Multiply 0 and 3 to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{C}
This is true for any x.
0x+0y=0\times 3
Do the multiplications.
0+0y=0\times 3
Anything times zero gives zero.
0+0=0\times 3
Anything times zero gives zero.
0=0\times 3
Add 0 and 0 to get 0.
0=0
Multiply 0 and 3 to get 0.
\text{true}
Compare 0 and 0.
y\in \mathrm{C}
This is true for any y.
0x+0y=0\times 3
Do the multiplications.
0+0y=0\times 3
Anything times zero gives zero.
0+0=0\times 3
Anything times zero gives zero.
0=0\times 3
Add 0 and 0 to get 0.
0=0
Multiply 0 and 3 to get 0.
\text{true}
Compare 0 and 0.
x\in \mathrm{R}
This is true for any x.
0x+0y=0\times 3
Do the multiplications.
0+0y=0\times 3
Anything times zero gives zero.
0+0=0\times 3
Anything times zero gives zero.
0=0\times 3
Add 0 and 0 to get 0.
0=0
Multiply 0 and 3 to get 0.
\text{true}
Compare 0 and 0.
y\in \mathrm{R}
This is true for any y.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
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}