Divide Using Long Polynomial Division square root of 3 , 3i

$\sqrt{3}$ , $3 i$

Step 1

Rewrite the division as a fraction.

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

Step 2

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

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

Step 3

Multiply.

Combine.

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

Simplify the denominator.

Add parentheses.

$\frac{\sqrt{3} i}{3 (i i)}$

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

$\frac{\sqrt{3} i}{3 (i^{1} i)}$

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

$\frac{\sqrt{3} i}{3 (i^{1} i^{1})}$

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

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

Add $1$ and $1$ .

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

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

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

Step 4

Multiply $3$ by $- 1$ .

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

Step 5

Move the negative in front of the fraction.

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