Simplify (3+5i)^2

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

Step 1

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

$(3 + 5 i) (3 + 5 i)$

Step 2

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

Apply the distributive property.

$3 (3 + 5 i) + 5 i (3 + 5 i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $3$ by $3$ .

$9 + 3 (5 i) + 5 i \cdot 3 + 5 i (5 i)$

Multiply $5$ by $3$ .

$9 + 15 i + 5 i \cdot 3 + 5 i (5 i)$

Multiply $3$ by $5$ .

$9 + 15 i + 15 i + 5 i (5 i)$

Multiply $5 i (5 i)$ .

Multiply $5$ by $5$ .

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

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

$9 + 15 i + 15 i + 25 (i^{1} i)$

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

$9 + 15 i + 15 i + 25 (i^{1} i^{1})$

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

$9 + 15 i + 15 i + 25 i^{1 + 1}$

Add $1$ and $1$ .

$9 + 15 i + 15 i + 25 i^{2}$

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

$9 + 15 i + 15 i + 25 \cdot - 1$

Multiply $25$ by $- 1$ .

$9 + 15 i + 15 i - 25$

Subtract $25$ from $9$ .

$- 16 + 15 i + 15 i$

Add $15 i$ and $15 i$ .

$- 16 + 30 i$