simplify (4-2i)/i — step-by-step solution

Let's simplify:

\frac{4 - 2 i}{i}

ⓘ To remove i from the denominator, multiply the numerator and the denominator by i, since i*i = -1:

\frac{4 - 2 i}{i}

- i \times (4 - 2 i)

- i \times (4 - 2 i)

ⓘ Expand by multiplying each term inside the parentheses:

- i \times (4 - 2 i)

- (i \times 4 - 2 i^{2})

- (i \times 4 - 2 i^{2})

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (i \times 4 - 2 \times (-1))

- i \times 4 + 2 \times (-1)

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

i^{2}

-1

- i \times 4 + 2 \times (-1)

ⓘ Multiplications are done before additions and subtractions. A single minus sign does not cancel out, the product of a negative number by a positive number is negative:

2 \times (-1)

-2

- i \times 4 - 2

ⓘ A complex number is written in algebraic form a + b*i, a being its real part and b its imaginary part:

- i \times 4

- 4 i

▶Simplified form:

- 2 - 4 i