Solve for w a=iw

$a = i w$

Rewrite the equation as $i w = a$ .

$i w = a$

Divide each term in $i w = a$ by $i$ and simplify.

Divide each term in $i w = a$ by $i$ .

$\frac{i w}{i} = \frac{a}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i w}{i} = \frac{a}{i}$

Divide $w$ by $1$ .

$w = \frac{a}{i}$

Simplify the right side.

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

$w = \frac{a}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$w = \frac{a i}{i i}$

Simplify the denominator.

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

$w = \frac{a i}{i^{1} i}$

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

$w = \frac{a i}{i^{1} i^{1}}$

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

$w = \frac{a i}{i^{1 + 1}}$

Add $1$ and $1$ .

$w = \frac{a i}{i^{2}}$

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

$w = \frac{a i}{- 1}$

Move the negative one from the denominator of $\frac{a i}{- 1}$ .

$w = - 1 \cdot (a i)$

Rewrite $- 1 \cdot (a i)$ as $- (a i)$ .

$w = - a i$