Basic Math Examples

$(- 2 + 4 i) \cdot (5 i)$

Step 1

Apply the distributive property.

$- 2 (5 i) + 4 i (5 i)$

Step 2

Multiply $5$ by $- 2$ .

$- 10 i + 4 i (5 i)$

Step 3

Multiply $4 i (5 i)$ .

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Step 3.1

Multiply $5$ by $4$ .

$- 10 i + 20 i i$

Step 3.2

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

$- 10 i + 20 (i^{1} i)$

Step 3.3

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

$- 10 i + 20 (i^{1} i^{1})$

Step 3.4

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

$- 10 i + 20 i^{1 + 1}$

Step 3.5

Add $1$ and $1$ .

$- 10 i + 20 i^{2}$

Step 4

Simplify each term.

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Step 4.1

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

$- 10 i + 20 \cdot - 1$

Step 4.2

Multiply $20$ by $- 1$ .

$- 10 i - 20$

Step 5

Reorder $- 10 i$ and $- 20$ .

$- 20 - 10 i$