Finite Math Examples

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

Step 1

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

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

Step 2

Multiply.

Tap for more steps...

Step 2.1

Combine.

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

Step 2.2

Simplify the numerator.

Tap for more steps...

Step 2.2.1

Apply the distributive property.

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

Step 2.2.2

Multiply $- 5 i i$ .

Tap for more steps...

Step 2.2.2.1

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

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

Step 2.2.2.2

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

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

Step 2.2.2.3

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

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

Step 2.2.2.4

Add $1$ and $1$ .

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

Step 2.2.3

Simplify each term.

Tap for more steps...

Step 2.2.3.1

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

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

Step 2.2.3.2

Multiply $- 5$ by $- 1$ .

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

Step 2.2.4

Reorder $6 i$ and $5$ .

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

Step 2.3

Simplify the denominator.

Tap for more steps...

Step 2.3.1

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

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

Step 2.3.2

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

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

Step 2.3.3

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

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

Step 2.3.4

Add $1$ and $1$ .

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

Step 2.3.5

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

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

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Move the negative one from the denominator of $\frac{5 + 6 i}{- 1}$ .

$- 1 \cdot (5 + 6 i)$

Step 3.2

Rewrite $- 1 \cdot (5 + 6 i)$ as $- (5 + 6 i)$ .

$- (5 + 6 i)$

Step 4

Apply the distributive property.

$- 1 \cdot 5 - (6 i)$

Step 5

Multiply.

Tap for more steps...

Step 5.1

Multiply $- 1$ by $5$ .

$- 5 - (6 i)$

Step 5.2

Multiply $6$ by $- 1$ .

$- 5 - 6 i$