Precalculus Examples

$7 i (- 4 i - 3) - 6 (- 3 + 5 i)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 i (- 4 i) + 7 i \cdot - 3 - 6 (- 3 + 5 i)$

Step 1.2

Multiply $7 i (- 4 i)$ .

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Step 1.2.1

Multiply $- 4$ by $7$ .

$- 28 i i + 7 i \cdot - 3 - 6 (- 3 + 5 i)$

Step 1.2.2

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

$- 28 (i^{1} i) + 7 i \cdot - 3 - 6 (- 3 + 5 i)$

Step 1.2.3

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

$- 28 (i^{1} i^{1}) + 7 i \cdot - 3 - 6 (- 3 + 5 i)$

Step 1.2.4

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

$- 28 i^{1 + 1} + 7 i \cdot - 3 - 6 (- 3 + 5 i)$

Step 1.2.5

Add $1$ and $1$ .

$- 28 i^{2} + 7 i \cdot - 3 - 6 (- 3 + 5 i)$

Step 1.3

Multiply $- 3$ by $7$ .

$- 28 i^{2} - 21 i - 6 (- 3 + 5 i)$

Step 1.4

Simplify each term.

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Step 1.4.1

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

$- 28 \cdot - 1 - 21 i - 6 (- 3 + 5 i)$

Step 1.4.2

Multiply $- 28$ by $- 1$ .

$28 - 21 i - 6 (- 3 + 5 i)$

Step 1.5

Apply the distributive property.

$28 - 21 i - 6 \cdot - 3 - 6 (5 i)$

Step 1.6

Multiply $- 6$ by $- 3$ .

$28 - 21 i + 18 - 6 (5 i)$

Step 1.7

Multiply $5$ by $- 6$ .

$28 - 21 i + 18 - 30 i$

Step 2

Simplify by adding terms.

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Step 2.1

Add $28$ and $18$ .

$46 - 21 i - 30 i$

Step 2.2

Subtract $30 i$ from $- 21 i$ .

$46 - 51 i$