Solve for r e=ir

$e = i r$

Step 1

Rewrite the equation as $i r = e$ .

$i r = e$

Step 2

Divide each term in $i r = e$ by $i$ and simplify.

Divide each term in $i r = e$ by $i$ .

$\frac{i r}{i} = \frac{e}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i r}{i} = \frac{e}{i}$

Divide $r$ by $1$ .

$r = \frac{e}{i}$

Simplify the right side.

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

$r = \frac{e}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$r = \frac{e i}{i i}$

Simplify the denominator.

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

$r = \frac{e i}{i^{1} i}$

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

$r = \frac{e i}{i^{1} i^{1}}$

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

$r = \frac{e i}{i^{1 + 1}}$

Add $1$ and $1$ .

$r = \frac{e i}{i^{2}}$

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

$r = \frac{e i}{- 1}$

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

$r = - 1 \cdot (e i)$

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

$r = - e i$