Let's reduce: $\frac{-4+6i}{2+7i}$

ⓘ To make the denominator real, multiply the numerator and denominator by its conjugate, since (a+bi)(a-bi) = a²+b²: $\frac{-4+6i}{2+7i}$ = $\frac{(-4+6i)\times (2-7i)}{2^2+7^2}$

$\frac{(-4+6i)\times (2-7i)}{2^2+7^2}$

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product: $2^2$ = $2\times 2$ = $4$, $7^2$ = $7\times 7$ = $49$

$\frac{(-4+6i)\times (2-7i)}{4+49}$

ⓘ The numerator and the denominator are computed before the division: $4+49$ = $53$

$\frac{(-4+6i)\times (2-7i)}{53}$

ⓘ Expand by multiplying each term inside the parentheses: $(-4+6i)\times (2-7i)$ = $-4\times 2$$-4\times \left(-7\right)i$$+6i\times 2$$+6\times i\times \left(-7\right)\times i$

$\frac{-4\times 2-4\times \left(-7\right)i+6i\times 2+6\times i\times \left(-7\right)\times i}{53}$

ⓘ Multiplications are done before additions and subtractions: $4\times 2$ = $8$, $6\times 2$ = $12$■Multiplications are done before additions and subtractions. Two minus signs cancel out, the product of two negative numbers is positive: $-4\times \left(-7\right)$ = $28$■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: $6\times \left(-7\right)$ = $-42$■Multiplying powers with the same base adds the exponents: $i\times i$ = $i^2$

$\frac{-8+28i+12i-42i^2}{53}$

ⓘ Like terms are grouped by adding their coefficients: $28i+12i$ = $40i$■Multiplying by -1 gives the opposite: $-42\times \left(-1\right)$ = $42$■i^2 = -1, so the powers of i reduce to 1, i, -1 or -i: $i^2$ = $-1$

$\frac{-8+40i+42}{53}$

ⓘ The numerator and the denominator are computed before the division: $-8+42$ = $34$

$\frac{34+40i}{53}$

ⓘ A complex number is written in algebraic form a + b*i, a being its real part and b its imaginary part: $\frac{34+40i}{53}$ = $\frac{34}{53}+\frac{40}{53}\times i$

▶Simplified form:   $\frac{34}{53}+\frac{40}{53}\times i$

The numeric value of: $\frac{34}{53}+\frac{40}{53}\times i$ equals:

▷ $\approx 0.6415+\approx 0.7547i$