Write in Standard Form (6+5i)/(-2i)

$\frac{6 + 5 i}{- 2 i}$

Step 1

Multiply the numerator and denominator of $\frac{6 + 5 i}{- 2 i}$ by the conjugate of $- 2 i$ to make the denominator real.

$\frac{6 + 5 i}{- 2 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(6 + 5 i) i}{- 2 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{6 i + 5 i i}{- 2 i i}$

Multiply $5 i i$ .

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

$\frac{6 i + 5 (i^{1} i)}{- 2 i i}$

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

$\frac{6 i + 5 (i^{1} i^{1})}{- 2 i i}$

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

$\frac{6 i + 5 i^{1 + 1}}{- 2 i i}$

Add $1$ and $1$ .

$\frac{6 i + 5 i^{2}}{- 2 i i}$

Simplify each term.

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

$\frac{6 i + 5 \cdot - 1}{- 2 i i}$

Multiply $5$ by $- 1$ .

$\frac{6 i - 5}{- 2 i i}$

Reorder $6 i$ and $- 5$ .

$\frac{- 5 + 6 i}{- 2 i i}$

Simplify the denominator.

Add parentheses.

$\frac{- 5 + 6 i}{- 2 (i i)}$

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

$\frac{- 5 + 6 i}{- 2 (i^{1} i)}$

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

$\frac{- 5 + 6 i}{- 2 (i^{1} i^{1})}$

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

$\frac{- 5 + 6 i}{- 2 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{- 5 + 6 i}{- 2 i^{2}}$

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

$\frac{- 5 + 6 i}{- 2 \cdot - 1}$

Step 3

Multiply $- 2$ by $- 1$ .

$\frac{- 5 + 6 i}{2}$

Step 4

Split the fraction $\frac{- 5 + 6 i}{2}$ into two fractions.

$\frac{- 5}{2} + \frac{6 i}{2}$

Step 5

Simplify each term.

Move the negative in front of the fraction.

$- \frac{5}{2} + \frac{6 i}{2}$

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

Factor $2$ out of $6 i$ .

$- \frac{5}{2} + \frac{2 (3 i)}{2}$

Cancel the common factors.

Factor $2$ out of $2$ .

$- \frac{5}{2} + \frac{2 (3 i)}{2 (1)}$

Cancel the common factor.

$- \frac{5}{2} + \frac{2 (3 i)}{2 \cdot 1}$

Rewrite the expression.

$- \frac{5}{2} + \frac{3 i}{1}$

Divide $3 i$ by $1$ .

$- \frac{5}{2} + 3 i$

Write in Standard Form (6+5i)/(-2i)

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