Solve 6+8sqrt{-1}=a+ib

$$6 + 8 \sqrt { - 1 } = a + i b$$

Solve for a

$$a=6+8i-ib$$

Solution Steps

Calculate the square root of -1 and get i.

$$6+8i=a+ib$$

Swap sides so that all variable terms are on the left hand side.

$$a+ib=6+8i$$

Subtract ib from both sides.

$$a=6+8i-ib$$

Reorder the terms.

$$a=-ib+\left(6+8i\right)$$

Solve for b

$$b=ia+\left(8-6i\right)$$

Steps for Solving Linear Equation

Calculate the square root of -1 and get i.

$$6+8i=a+ib$$

Swap sides so that all variable terms are on the left hand side.

$$a+ib=6+8i$$

Subtract a from both sides.

$$ib=6+8i-a$$

Divide both sides by i.

$$\frac{ib}{i}=\frac{6+8i-a}{i}$$

Dividing by i undoes the multiplication by i.

$$b=\frac{6+8i-a}{i}$$

Divide 6+8i-a by i.

$$b=ia+\left(8-6i\right)$$