Solve for z 6ib=coz

$6 i b = c oz$

Step 1

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

Divide each term in $6 i b = c oz$ by $6 i$ .

$\frac{6 i b}{6 i} = \frac{c oz}{6 i}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 i b}{6 i} = \frac{c oz}{6 i}$

Rewrite the expression.

$\frac{i b}{i} = \frac{c oz}{6 i}$

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i b}{i} = \frac{c oz}{6 i}$

Divide $b$ by $1$ .

$b = \frac{c oz}{6 i}$

Simplify the right side.

Multiply the numerator and denominator of $\frac{c oz}{6 i}$ by the conjugate of $6 i$ to make the denominator real.

$b = \frac{c oz}{6 i} \cdot \frac{i}{i}$

Multiply.

Combine.

$b = \frac{c oz i}{6 i i}$

Simplify the denominator.

Add parentheses.

$b = \frac{c oz i}{6 (i i)}$

Raise $i$ to the power of $1$ .

$b = \frac{c oz i}{6 (i^{1} i)}$

Raise $i$ to the power of $1$ .

$b = \frac{c oz i}{6 (i^{1} i^{1})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$b = \frac{c oz i}{6 i^{1 + 1}}$

Add $1$ and $1$ .

$b = \frac{c oz i}{6 i^{2}}$

Rewrite $i^{2}$ as $- 1$ .

$b = \frac{c oz i}{6 \cdot - 1}$

Multiply $6$ by $- 1$ .

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

Move the negative in front of the fraction.

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

Step 2

Rewrite the expression.

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