(1+i)^2 — step-by-step solution

Let's calculate:

{(1 + i)}^{2}

ⓘ Raising a sum to a positive integer power means multiplying it by itself as many times as the exponent indicates:

{(1 + i)}^{2}

(1 + i) \times (1 + i)

(1 + i) \times (1 + i)

ⓘ Multiply each term of the sum by the other factor, using the distributive law:

(1 + i) \times (1 + i)

1 \times 1

+ 1 \times i

+ i \times 1

+ i \times i

1 \times 1

+ 1 \times i

+ i \times 1

+ i \times i

ⓘ Perform multiplications before additions and subtractions:

1 \times 1

1

■Multiplying powers with the same base adds the exponents:

i \times i

i^{2}

1

+ i

+ i

+ i^{2}

ⓘ Group like terms by adding their coefficients:

i + i

2 i

■

i^{2} = -1

, so integer powers of i reduce to

1

i

-1

- i

i^{2}

-1

1 + 2 i - 1

ⓘ Start from

1

and move back

1

on the number line, down to zero:

1 - 1

0

0 + 2 i

ⓘ Adding 0 changes nothing:

0 + 2 i

2 i

▶Result:

2 i