Algebra Examples

${(3 - 4 i)}^{2}$

Step 1

Rewrite ${(3 - 4 i)}^{2}$ as $(3 - 4 i) (3 - 4 i)$ .

$(3 - 4 i) (3 - 4 i)$

Step 2

Expand $(3 - 4 i) (3 - 4 i)$ using the FOIL Method.

Tap for more steps...

Step 2.1

Apply the distributive property.

$3 (3 - 4 i) - 4 i (3 - 4 i)$

Step 2.2

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 i) - 4 i (3 - 4 i)$

Step 2.3

Apply the distributive property.

$3 \cdot 3 + 3 (- 4 i) - 4 i \cdot 3 - 4 i (- 4 i)$

Step 3

Simplify and combine like terms.

Tap for more steps...

Step 3.1

Simplify each term.

Tap for more steps...

Step 3.1.1

Multiply $3$ by $3$ .

$9 + 3 (- 4 i) - 4 i \cdot 3 - 4 i (- 4 i)$

Step 3.1.2

Multiply $- 4$ by $3$ .

$9 - 12 i - 4 i \cdot 3 - 4 i (- 4 i)$

Step 3.1.3

Multiply $3$ by $- 4$ .

$9 - 12 i - 12 i - 4 i (- 4 i)$

Step 3.1.4

Multiply $- 4 i (- 4 i)$ .

Tap for more steps...

Step 3.1.4.1

Multiply $- 4$ by $- 4$ .

$9 - 12 i - 12 i + 16 i i$

Step 3.1.4.2

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

$9 - 12 i - 12 i + 16 (i^{1} i)$

Step 3.1.4.3

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

$9 - 12 i - 12 i + 16 (i^{1} i^{1})$

Step 3.1.4.4

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

$9 - 12 i - 12 i + 16 i^{1 + 1}$

Step 3.1.4.5

Add $1$ and $1$ .

$9 - 12 i - 12 i + 16 i^{2}$

Step 3.1.5

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

$9 - 12 i - 12 i + 16 \cdot - 1$

Step 3.1.6

Multiply $16$ by $- 1$ .

$9 - 12 i - 12 i - 16$

Step 3.2

Subtract $16$ from $9$ .

$- 7 - 12 i - 12 i$

Step 3.3

Subtract $12 i$ from $- 12 i$ .

$- 7 - 24 i$