Solve for t
t=\frac{y+\left(-2-6i\right)}{345}
Solve for y
y=345t+\left(2+6i\right)
Share
Copied to clipboard
345it=6-2i+yi
Add yi to both sides.
345it=iy+\left(6-2i\right)
The equation is in standard form.
\frac{345it}{345i}=\frac{iy+\left(6-2i\right)}{345i}
Divide both sides by 345i.
t=\frac{iy+\left(6-2i\right)}{345i}
Dividing by 345i undoes the multiplication by 345i.
t=\frac{y}{345}+\left(-\frac{2}{345}-\frac{2}{115}i\right)
Divide 6-2i+iy by 345i.
345it-iy=6-2i
Multiply -1 and i to get -i.
-iy=6-2i-345it
Subtract 345it from both sides.
\frac{-iy}{-i}=\frac{6-2i-345it}{-i}
Divide both sides by -i.
y=\frac{6-2i-345it}{-i}
Dividing by -i undoes the multiplication by -i.
y=345t+\left(2+6i\right)
Divide 6-2i-345it by -i.
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}