Solve Lambda+iw=(w)

$$\Lambda + i w = ( w )$$

Solve for w

$$w=\left(\frac{1}{2}+\frac{1}{2}i\right)\Lambda$$

Steps for Solving Linear Equation

Subtract w from both sides.

$$\Lambda +iw-w=0$$

Combine iw and -w to get \left(-1+i\right)w.

$$\Lambda +\left(-1+i\right)w=0$$

Subtract \Lambda from both sides. Anything subtracted from zero gives its negation.

$$\left(-1+i\right)w=-\Lambda$$

Divide both sides by -1+i.

$$\frac{\left(-1+i\right)w}{-1+i}=-\frac{\Lambda }{-1+i}$$

Dividing by -1+i undoes the multiplication by -1+i.

$$w=-\frac{\Lambda }{-1+i}$$

Divide -\Lambda by -1+i.

$$w=\left(\frac{1}{2}+\frac{1}{2}i\right)\Lambda$$

Solve for Λ

$$\Lambda =\left(1-i\right)w$$

Solution Steps

Subtract iw from both sides.

$$\Lambda =w-iw$$

Combine w and -iw to get \left(1-i\right)w.

$$\Lambda =\left(1-i\right)w$$