simplify (-1-3i)*(-1+i) — step-by-step solution

Let's simplify:

(- 1 - 3 i) \times (- 1 + i)

ⓘ Expand by multiplying each term inside the parentheses:

(- 1 - 3 i) \times (- 1 + i)

- 1 \times (-1)

- 1 \times i

- 3 i \times (-1)

- 3 \times i \times i

- 1 \times (-1)

- 1 \times i

- 3 i \times (-1)

- 3 \times i \times i

ⓘ Multiplications are done before additions and subtractions. Two minus signs cancel out, the product of two negative numbers is positive:

-1 \times (-1)

1

-3 \times (-1)

3

■Multiplying by 1 changes nothing:

1 \times i

i

■Multiplying powers with the same base adds the exponents:

i \times i

i^{2}

1

- i

+ 3 i

- 3 i^{2}

ⓘ Like terms are grouped by adding their coefficients:

- i + 3 i

2 i

■Multiplying by -1 gives the opposite:

- 3 \times (-1)

3

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

i^{2}

-1

1 + 2 i + 3

ⓘ Start from

1

and move forward

3

on the number line:

1 + 3

4

▶Simplified form:

4 + 2 i