Simplify (5+yi)^2

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

Step 1

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

$(5 + y i) (5 + y i)$

Step 2

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

Apply the distributive property.

$5 (5 + y i) + y i (5 + y i)$

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

$25 + 5 (y i) + y i \cdot 5 + y i (y i)$

Move $5$ to the left of $y i$ .

$25 + 5 y i + 5 \cdot (y i) + y i (y i)$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$25 + 5 y i + 5 y i + y \cdot y i i$

Multiply $y$ by $y$ .

$25 + 5 y i + 5 y i + y^{2} i i$

Multiply $y^{2} i i$ .

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

$25 + 5 y i + 5 y i + y^{2} (i^{1} i)$

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

$25 + 5 y i + 5 y i + y^{2} (i^{1} i^{1})$

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

$25 + 5 y i + 5 y i + y^{2} i^{1 + 1}$

Add $1$ and $1$ .

$25 + 5 y i + 5 y i + y^{2} i^{2}$

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

$25 + 5 y i + 5 y i + y^{2} \cdot - 1$

Move $- 1$ to the left of $y^{2}$ .

$25 + 5 y i + 5 y i - 1 \cdot y^{2}$

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

$25 + 5 y i + 5 y i - y^{2}$

Add $5 y i$ and $5 y i$ .

$25 + 10 y i - y^{2}$