Solution - Absolute value equations

$$\left(-4i+3\right)=-3i-4$$

Add $$$$ to both sides:

$$\left(-4i+3\right)+3i=\left(-3i-4\right)+3i$$

Group like terms:

$$\left(-4i+3i\right)+3=\left(-3i-4\right)+3i$$

Simplify the arithmetic:

$$-i+3=\left(-3i-4\right)+3i$$

Group like terms:

$$-i+3=\left(-3i+3i\right)-4$$

Simplify the arithmetic:

$$-i+3=-4$$

Subtract $$$$ from both sides:

$$\left(-i+3\right)-3=-4-3$$

Simplify the arithmetic:

$$-i=-4-3$$

Simplify the arithmetic:

$$-i=-7$$

Multiply both sides by $$$$:

$$-i·-1=-7·-1$$

Remove the one(s):

$$i=-7·-1$$

Simplify the arithmetic:

$$i=7$$

$$\left(-4i+3\right)=3i+4$$

Subtract $$$$ from both sides:

$$\left(-4i+3\right)-3i=\left(3i+4\right)-3i$$

Group like terms:

$$\left(-4i-3i\right)+3=\left(3i+4\right)-3i$$

Simplify the arithmetic:

$$-7i+3=\left(3i+4\right)-3i$$

Group like terms:

$$-7i+3=\left(3i-3i\right)+4$$

Simplify the arithmetic:

$$-7i+3=4$$

Subtract $$$$ from both sides:

$$\left(-7i+3\right)-3=4-3$$

Simplify the arithmetic:

$$-7i=4-3$$

Simplify the arithmetic:

$$-7i=1$$

Divide both sides by :

$$\frac{\left(-7i\right)}{-7}=\frac{1}{-7}$$

Cancel out the negatives:

$$\frac{7i}{7}=\frac{1}{-7}$$

Simplify the fraction:

$$i=\frac{1}{-7}$$

Move the negative sign from the denominator to the numerator:

$$i=\frac{-1}{7}$$