Solve zi=2+i

$$z i = 2 + i$$

Solve for z

$$z=1-2i$$

Steps for Solving Linear Equation

Divide both sides by i.

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

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

$$z=\frac{\left(2+i\right)i}{1i^{2}}$$

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

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

Multiply 2+i times i.

$$z=\frac{2i+i^{2}}{-1}$$

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

$$z=\frac{2i-1}{-1}$$

Reorder the terms.

$$z=\frac{-1+2i}{-1}$$

Divide -1+2i by -1 to get 1-2i.

$$z=1-2i$$