Solve for f if=M

$i f = M$

Divide each term in $i f = M$ by $i$ .

$\frac{i f}{i} = \frac{M}{i}$

Simplify the left side.

Cancel the common factor of $i$ .

Cancel the common factor.

$\frac{i f}{i} = \frac{M}{i}$

Divide $f$ by $1$ .

$f = \frac{M}{i}$

Simplify the right side.

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

$f = \frac{M}{i} \cdot \frac{i}{i}$

Multiply.

Combine.

$f = \frac{M i}{i i}$

Simplify the denominator.

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

$f = \frac{M i}{i^{1} i}$

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

$f = \frac{M i}{i^{1} i^{1}}$

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

$f = \frac{M i}{i^{1 + 1}}$

Add $1$ and $1$ .

$f = \frac{M i}{i^{2}}$

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

$f = \frac{M i}{- 1}$

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

$f = - 1 \cdot (M i)$

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

$f = - M i$