Solve 3iz-2i=4

$$3 i z - 2 i = 4$$

Solve for z

$$z=\frac{2}{3}-\frac{4}{3}i\approx 0.666666667-1.333333333i$$

Steps for Solving Linear Equation

Add 2i to both sides.

$$3iz=4+2i$$

Divide both sides by 3i.

$$z=\frac{4+2i}{3i}$$

Multiply both numerator and denominator of \frac{4+2i}{3i} by imaginary unit i.

$$z=\frac{\left(4+2i\right)i}{3i^{2}}$$

By definition, i^{2} is -1. Calculate the denominator.

$$z=\frac{\left(4+2i\right)i}{-3}$$

Multiply 4+2i times i.

$$z=\frac{4i+2i^{2}}{-3}$$

By definition, i^{2} is -1.

$$z=\frac{4i+2\left(-1\right)}{-3}$$

Do the multiplications in 4i+2\left(-1\right). Reorder the terms.

$$z=\frac{-2+4i}{-3}$$

Divide -2+4i by -3 to get \frac{2}{3}-\frac{4}{3}i.

$$z=\frac{2}{3}-\frac{4}{3}i$$