Solve for R iR=V

$i R = V$

Step 1

Divide each term in $i R = V$ by $i$ .

$\frac{i R}{i} = \frac{V}{i}$

Step 2

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i R}{i} = \frac{V}{i}$

Divide $R$ by $1$ .

$R = \frac{V}{i}$

Step 3

Simplify the right side.

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

$R = \frac{V}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$R = \frac{V i}{i i}$

Simplify the denominator.

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

$R = \frac{V i}{i^{1} i}$

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

$R = \frac{V i}{i^{1} i^{1}}$

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

$R = \frac{V i}{i^{1 + 1}}$

Add $1$ and $1$ .

$R = \frac{V i}{i^{2}}$

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

$R = \frac{V i}{- 1}$

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

$R = - 1 \cdot (V i)$

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

$R = - V i$