Solve 3+5i+-yi=6-2i

$$3 + 5 i + - y i = 6 - 2 i$$

Solve for y

$$y=7+3i$$

Steps for Solving Linear Equation

Subtract 3+5i from both sides.

$$\left(-y\right)i=6-2i-\left(3+5i\right)$$

Subtract 3+5i from 6-2i by subtracting corresponding real and imaginary parts.

$$\left(-y\right)i=6-3+\left(-2-5\right)i$$

Subtract 3 from 6. Subtract 5 from -2.

$$\left(-y\right)i=3-7i$$

Divide both sides by i.

$$-y=\frac{3-7i}{i}$$

Multiply both numerator and denominator of \frac{3-7i}{i} by imaginary unit i.

$$-y=\frac{\left(3-7i\right)i}{1i^{2}}$$

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

$$-y=\frac{\left(3-7i\right)i}{-1}$$

Multiply 3-7i times i.

$$-y=\frac{3i-7i^{2}}{-1}$$

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

$$-y=\frac{3i-7\left(-1\right)}{-1}$$

Do the multiplications in 3i-7\left(-1\right). Reorder the terms.

$$-y=\frac{7+3i}{-1}$$

Divide 7+3i by -1 to get -7-3i.

$$-y=-7-3i$$

Divide both sides by -1.

$$y=\frac{-7-3i}{-1}$$

Divide -7-3i by -1 to get 7+3i.

$$y=7+3i$$