Evaluate 6/(2i)

$\frac{6}{2 i}$

Step 1

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6$ .

$\frac{2 \cdot 3}{2 i}$

Cancel the common factors.

Factor $2$ out of $2 i$ .

$\frac{2 \cdot 3}{2 (i)}$

Cancel the common factor.

$\frac{2 \cdot 3}{2 i}$

Rewrite the expression.

$\frac{3}{i}$

Step 2

Multiply the numerator and denominator of $\frac{3}{i}$ by the conjugate of $i$ to make the denominator real.

$\frac{3}{i} \cdot \frac{i}{i}$

Step 3

Multiply.

Combine.

$\frac{3 i}{i i}$

Simplify the denominator.

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

$\frac{3 i}{i^{1} i}$

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

$\frac{3 i}{i^{1} i^{1}}$

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

$\frac{3 i}{i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{3 i}{i^{2}}$

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

$\frac{3 i}{- 1}$

Step 4

Move the negative one from the denominator of $\frac{3 i}{- 1}$ .

$- 1 \cdot (3 i)$

Step 5

Rewrite $- 1 \cdot (3 i)$ as $- (3 i)$ .

$- (3 i)$

Step 6

Multiply $3$ by $- 1$ .

$- 3 i$