Simplify (7-13i)/(2i)

$\frac{7 - 13 i}{2 i}$

Step 1

Multiply the numerator and denominator of $\frac{7 - 13 i}{2 i}$ by the conjugate of $2 i$ to make the denominator real.

$\frac{7 - 13 i}{2 i} \cdot \frac{i}{i}$

Step 2

Multiply.

Combine.

$\frac{(7 - 13 i) i}{2 i i}$

Simplify the numerator.

Apply the distributive property.

$\frac{7 i - 13 i i}{2 i i}$

Multiply $- 13 i i$ .

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

$\frac{7 i - 13 (i^{1} i)}{2 i i}$

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

$\frac{7 i - 13 (i^{1} i^{1})}{2 i i}$

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

$\frac{7 i - 13 i^{1 + 1}}{2 i i}$

Add $1$ and $1$ .

$\frac{7 i - 13 i^{2}}{2 i i}$

Simplify each term.

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

$\frac{7 i - 13 \cdot - 1}{2 i i}$

Multiply $- 13$ by $- 1$ .

$\frac{7 i + 13}{2 i i}$

Reorder $7 i$ and $13$ .

$\frac{13 + 7 i}{2 i i}$

Simplify the denominator.

Add parentheses.

$\frac{13 + 7 i}{2 (i i)}$

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

$\frac{13 + 7 i}{2 (i^{1} i)}$

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

$\frac{13 + 7 i}{2 (i^{1} i^{1})}$

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

$\frac{13 + 7 i}{2 i^{1 + 1}}$

Add $1$ and $1$ .

$\frac{13 + 7 i}{2 i^{2}}$

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

$\frac{13 + 7 i}{2 \cdot - 1}$

Step 3

Multiply $2$ by $- 1$ .

$\frac{13 + 7 i}{- 2}$

Step 4

Split the fraction $\frac{13 + 7 i}{- 2}$ into two fractions.

$\frac{13}{- 2} + \frac{7 i}{- 2}$

Step 5

Simplify each term.

Move the negative in front of the fraction.

$- \frac{13}{2} + \frac{7 i}{- 2}$

Move the negative in front of the fraction.

$- \frac{13}{2} - \frac{7 i}{2}$

Simplify (7-13i)/(2i)

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