Write in Standard Form (2+3i)/(2i)

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

Step 1

Multiply the numerator and denominator of $\frac{2 + 3 i}{2 i}$ by the conjugate of $2 i$ to make the denominator real.

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

Step 2

Multiply.

Combine.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $3 i i$ .

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

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

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

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

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

$\frac{2 i + 3 i^{1 + 1}}{2 i i}$

Add $1$ and $1$ .

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

Simplify each term.

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

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

Multiply $3$ by $- 1$ .

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

Reorder $2 i$ and $- 3$ .

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

Simplify the denominator.

Add parentheses.

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

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

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

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

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

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

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

Add $1$ and $1$ .

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

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

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

Step 3

Multiply $2$ by $- 1$ .

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

Step 4

Split the fraction $\frac{- 3 + 2 i}{- 2}$ into two fractions.

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

Step 5

Simplify each term.

Dividing two negative values results in a positive value.

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

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

Factor $2$ out of $2 i$ .

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

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

$\frac{3}{2} - 1 \cdot i$

Rewrite $- 1 \cdot i$ as $- i$ .

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

Write in Standard Form (2+3i)/(2i)

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