Basic Math Examples

$21 + 6 i (- 5 + 11 i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$21 + 6 i \cdot - 5 + 6 i (11 i)$

Step 1.2

Multiply $- 5$ by $6$ .

$21 - 30 i + 6 i (11 i)$

Step 1.3

Multiply $6 i (11 i)$ .

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Step 1.3.1

Multiply $11$ by $6$ .

$21 - 30 i + 66 i i$

Step 1.3.2

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

$21 - 30 i + 66 (i^{1} i)$

Step 1.3.3

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

$21 - 30 i + 66 (i^{1} i^{1})$

Step 1.3.4

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

$21 - 30 i + 66 i^{1 + 1}$

Step 1.3.5

Add $1$ and $1$ .

$21 - 30 i + 66 i^{2}$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$21 - 30 i + 66 \cdot - 1$

Step 1.4.2

Multiply $66$ by $- 1$ .

$21 - 30 i - 66$

Step 2

Subtract $66$ from $21$ .

$- 45 - 30 i$