Simplify (5+2i)^2+(2-i)^2

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

Simplify each term.

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

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

Expand $(5 + 2 i) (5 + 2 i)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Multiply $5$ by $5$ .

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

Multiply $2$ by $5$ .

$25 + 10 i + 2 i \cdot 5 + 2 i (2 i) + {(2 - i)}^{2}$

Multiply $5$ by $2$ .

$25 + 10 i + 10 i + 2 i (2 i) + {(2 - i)}^{2}$

Multiply $2 i (2 i)$ .

Multiply $2$ by $2$ .

$25 + 10 i + 10 i + 4 i i + {(2 - i)}^{2}$

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

$25 + 10 i + 10 i + 4 (i^{1} i) + {(2 - i)}^{2}$

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

$25 + 10 i + 10 i + 4 (i^{1} i^{1}) + {(2 - i)}^{2}$

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

$25 + 10 i + 10 i + 4 i^{1 + 1} + {(2 - i)}^{2}$

Add $1$ and $1$ .

$25 + 10 i + 10 i + 4 i^{2} + {(2 - i)}^{2}$

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

$25 + 10 i + 10 i + 4 \cdot - 1 + {(2 - i)}^{2}$

Multiply $4$ by $- 1$ .

$25 + 10 i + 10 i - 4 + {(2 - i)}^{2}$

Subtract $4$ from $25$ .

$21 + 10 i + 10 i + {(2 - i)}^{2}$

Add $10 i$ and $10 i$ .

$21 + 20 i + {(2 - i)}^{2}$

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

$21 + 20 i + (2 - i) (2 - i)$

Expand $(2 - i) (2 - i)$ using the FOIL Method.

Apply the distributive property.

$21 + 20 i + 2 (2 - i) - i (2 - i)$

Apply the distributive property.

$21 + 20 i + 2 \cdot 2 + 2 (- i) - i (2 - i)$

Apply the distributive property.

$21 + 20 i + 2 \cdot 2 + 2 (- i) - i \cdot 2 - i (- i)$

Simplify and combine like terms.

Simplify each term.

Multiply $2$ by $2$ .

$21 + 20 i + 4 + 2 (- i) - i \cdot 2 - i (- i)$

Multiply $- 1$ by $2$ .

$21 + 20 i + 4 - 2 i - i \cdot 2 - i (- i)$

Multiply $2$ by $- 1$ .

$21 + 20 i + 4 - 2 i - 2 i - i (- i)$

Multiply $- i (- i)$ .

Multiply $- 1$ by $- 1$ .

$21 + 20 i + 4 - 2 i - 2 i + 1 i i$

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

$21 + 20 i + 4 - 2 i - 2 i + 1 (i^{1} i)$

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

$21 + 20 i + 4 - 2 i - 2 i + 1 (i^{1} i^{1})$

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

$21 + 20 i + 4 - 2 i - 2 i + 1 i^{1 + 1}$

Add $1$ and $1$ .

$21 + 20 i + 4 - 2 i - 2 i + 1 i^{2}$

Multiply $i^{2}$ by $1$ .

$21 + 20 i + 4 - 2 i - 2 i + i^{2}$

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

$21 + 20 i + 4 - 2 i - 2 i - 1$

Subtract $1$ from $4$ .

$21 + 20 i + 3 - 2 i - 2 i$

Subtract $2 i$ from $- 2 i$ .

$21 + 20 i + 3 - 4 i$

Simplify by adding terms.

Add $21$ and $3$ .

$24 + 20 i - 4 i$

Subtract $4 i$ from $20 i$ .

$24 + 16 i$

Simplify (5+2i)^2+(2-i)^2

Related Questions

Support LCMGCF.com by disabling your adblocker.