Simplify (5i-3)^2

${(5 i - 3)}^{2}$

Step 1

Rewrite ${(5 i - 3)}^{2}$ as $(5 i - 3) (5 i - 3)$ .

$(5 i - 3) (5 i - 3)$

Step 2

Expand $(5 i - 3) (5 i - 3)$ using the FOIL Method.

Apply the distributive property.

$5 i (5 i - 3) - 3 (5 i - 3)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $5 i (5 i)$ .

Multiply $5$ by $5$ .

$25 i i + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

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

$25 (i^{1} i) + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

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

$25 (i^{1} i^{1}) + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

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

$25 i^{1 + 1} + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

Add $1$ and $1$ .

$25 i^{2} + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

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

$25 \cdot - 1 + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

Multiply $25$ by $- 1$ .

$- 25 + 5 i \cdot - 3 - 3 (5 i) - 3 \cdot - 3$

Multiply $- 3$ by $5$ .

$- 25 - 15 i - 3 (5 i) - 3 \cdot - 3$

Multiply $5$ by $- 3$ .

$- 25 - 15 i - 15 i - 3 \cdot - 3$

Multiply $- 3$ by $- 3$ .

$- 25 - 15 i - 15 i + 9$

Add $- 25$ and $9$ .

$- 16 - 15 i - 15 i$

Subtract $15 i$ from $- 15 i$ .

$- 16 - 30 i$