Linear Algebra Examples

$2 i (5 - 9 i)$

Step 1

Apply the distributive property.

$2 i \cdot 5 + 2 i (- 9 i)$

Step 2

Multiply $5$ by $2$ .

$10 i + 2 i (- 9 i)$

Step 3

Multiply $2 i (- 9 i)$ .

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Step 3.1

Multiply $- 9$ by $2$ .

$10 i - 18 i i$

Step 3.2

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

$10 i - 18 (i^{1} i)$

Step 3.3

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

$10 i - 18 (i^{1} i^{1})$

Step 3.4

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

$10 i - 18 i^{1 + 1}$

Step 3.5

Add $1$ and $1$ .

$10 i - 18 i^{2}$

Step 4

Simplify each term.

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Step 4.1

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

$10 i - 18 \cdot - 1$

Step 4.2

Multiply $- 18$ by $- 1$ .

$10 i + 18$

Step 5

Reorder $10 i$ and $18$ .

$18 + 10 i$