Solve for b (3+2i)+(2+bi)=5-4i

$(3 + 2 i) + (2 + b i) = 5 - 4 i$

Step 1

Add $3$ and $2$ .

$5 + 2 i + b i = 5 - 4 i$

Step 2

Move all terms not containing $b$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$2 i + b i = 5 - 4 i - 5$

Subtract $2 i$ from both sides of the equation.

$b i = 5 - 4 i - 5 - 2 i$

Subtract $5$ from $5$ .

$b i = 0 - 4 i - 2 i$

Subtract $4 i$ from $0$ .

$b i = - 4 i - 2 i$

Subtract $2 i$ from $- 4 i$ .

$b i = - 6 i$

Step 3

Divide each term in $b i = - 6 i$ by $i$ and simplify.

Divide each term in $b i = - 6 i$ by $i$ .

$\frac{b i}{i} = \frac{- 6 i}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{b i}{i} = \frac{- 6 i}{i}$

Divide $b$ by $1$ .

$b = \frac{- 6 i}{i}$

Simplify the right side.

Cancel the common factor of $i$ .

Cancel the common factor.

$b = \frac{- 6 i}{i}$

Divide $- 6$ by $1$ .

$b = - 6$