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

Let's simplify:

{(2 + i)}^{2}

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

{(2 + i)}^{2}

(2 + i) \times (2 + i)

(2 + i) \times (2 + i)

ⓘ Expand by multiplying each term inside the parentheses:

(2 + i) \times (2 + i)

2 \times 2

+ 2 i

+ i \times 2

+ i \times i

2 \times 2

+ 2 i

+ i \times 2

+ i \times i

ⓘ Multiplications are done before additions and subtractions:

2 \times 2

4

■Like terms are grouped by adding their coefficients:

2 i + i \times 2

4 i

■Multiplying powers with the same base adds the exponents:

i \times i

i^{2}

4 + 4 i + i^{2}

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

i^{2}

-1

4 + 4 i - 1

ⓘ Start from

4

and move back

1

on the number line:

4 - 1

3

▶Simplified form:

3 + 4 i