Basic Math Examples

$\frac{- 10 + 10 i}{2 i}$

Step 1

Cancel the common factor of $- 10 + 10 i$ and $2$ .

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Step 1.1

Factor $2$ out of $- 10$ .

$\frac{2 \cdot - 5 + 10 i}{2 i}$

Step 1.2

Factor $2$ out of $10 i$ .

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

Step 1.3

Factor $2$ out of $2 (- 5) + 2 (5 i)$ .

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

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $2 i$ .

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

Step 1.4.2

Cancel the common factor.

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

Step 1.4.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Multiply.

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Step 3.1

Combine.

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

Step 3.2

Simplify the numerator.

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Step 3.2.1

Apply the distributive property.

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

Step 3.2.2

Multiply $5 i i$ .

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Step 3.2.2.1

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

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

Step 3.2.2.2

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

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

Step 3.2.2.3

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

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

Step 3.2.2.4

Add $1$ and $1$ .

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

Step 3.2.3

Simplify each term.

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Step 3.2.3.1

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

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

Step 3.2.3.2

Multiply $5$ by $- 1$ .

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

Step 3.2.4

Reorder $- 5 i$ and $- 5$ .

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

Step 3.3

Simplify the denominator.

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Step 3.3.1

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

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

Step 3.3.2

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

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

Step 3.3.3

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

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

Step 3.3.4

Add $1$ and $1$ .

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

Step 3.3.5

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

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

Step 4

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

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

Step 5

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

$- (- 5 - 5 i)$

Step 6

Apply the distributive property.

$- - 5 - (- 5 i)$

Step 7

Multiply $- 1$ by $- 5$ .

$5 - (- 5 i)$

Step 8

Multiply $- 5$ by $- 1$ .

$5 + 5 i$