simplify (5-i)^2 — step-by-step solution

Let's simplify:

{(5 - i)}^{2}

ⓘ Raising a sum to an integer power is multiplying it by itself:

{(5 - i)}^{2}

(5 - i) \times (5 - i)

(5 - i) \times (5 - i)

ⓘ Expand by multiplying each term inside the parentheses:

(5 - i) \times (5 - i)

5 \times 5

+ 5 \times (- i)

- i \times 5

- i \times (- i)

5 \times 5

+ 5 \times (- i)

- i \times 5

- i \times (- i)

ⓘ Multiplications are done before additions and subtractions:

5 \times 5

25

■The minus sign is placed in front of the product:

5 \times (- i)

- 5 i

■Multiplying powers with the same base adds the exponents:

- i \times (- i)

{(- i)}^{2}

25

- 5 i

- i \times 5

+ {(- i)}^{2}

ⓘ Like terms are grouped by adding their coefficients:

- 5 i - i \times 5

-10 i

■i^2 = -1, so the powers of i reduce to 1, i, -1 or -i:

{(- i)}^{2}

-1

25 - 10 i - 1

ⓘ Start from

25

and move back

1

on the number line:

25 - 1

24

▶Simplified form:

24 - 10 i