Precalculus Examples

$- 7 i (3 i - 5)$

Step 1

Apply the distributive property.

$- 7 i (3 i) - 7 i \cdot - 5$

Step 2

Multiply $- 7 i (3 i)$ .

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Step 2.1

Multiply $3$ by $- 7$ .

$- 21 i i - 7 i \cdot - 5$

Step 2.2

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

$- 21 (i^{1} i) - 7 i \cdot - 5$

Step 2.3

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

$- 21 (i^{1} i^{1}) - 7 i \cdot - 5$

Step 2.4

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

$- 21 i^{1 + 1} - 7 i \cdot - 5$

Step 2.5

Add $1$ and $1$ .

$- 21 i^{2} - 7 i \cdot - 5$

Step 3

Multiply $- 5$ by $- 7$ .

$- 21 i^{2} + 35 i$

Step 4

Simplify each term.

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Step 4.1

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

$- 21 \cdot - 1 + 35 i$

Step 4.2

Multiply $- 21$ by $- 1$ .

$21 + 35 i$