Let's reduce: $\frac{4-3i}{3+2i}$

ⓘ To make the denominator real, multiply the numerator and denominator by its conjugate, since (a+bi)(a-bi) = a²+b²: $\frac{4-3i}{3+2i}$ = $\frac{(4-3i)\times (3-2i)}{3^2+2^2}$

$\frac{(4-3i)\times (3-2i)}{3^2+2^2}$

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product: $3^2$ = $3\times 3$ = $9$, $2^2$ = $2\times 2$ = $4$

$\frac{(4-3i)\times (3-2i)}{9+4}$

ⓘ The numerator and the denominator are computed before the division: $9+4$ = $13$

$\frac{(4-3i)\times (3-2i)}{13}$

ⓘ Expand by multiplying each term inside the parentheses: $(4-3i)\times (3-2i)$ = $4\times 3$$+4\times \left(-2\right)i$$-3\times i\times 3$$-3\times i\times \left(-2\right)\times i$

$\frac{4\times 3+4\times \left(-2\right)i-3\times i\times 3-3\times i\times \left(-2\right)\times i}{13}$

ⓘ Multiplications are done before additions and subtractions: $4\times 3$ = $12$, $3\times 3$ = $9$■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: $4\times \left(-2\right)$ = $-8$■Multiplications are done before additions and subtractions. Two minus signs cancel out, the product of two negative numbers is positive: $-3\times \left(-2\right)$ = $6$■Multiplying powers with the same base adds the exponents: $i\times i$ = $i^2$

$\frac{12-8i-9i+6i^2}{13}$

ⓘ Like terms are grouped by adding their coefficients: $-8i-9i$ = $-17i$■Multiplying by -1 gives the opposite: $6\times \left(-1\right)$ = $-6$■i^2 = -1, so the powers of i reduce to 1, i, -1 or -i: $i^2$ = $-1$

$\frac{12-17i-6}{13}$

ⓘ The numerator and the denominator are computed before the division: $12-6$ = $6$

$\frac{6-17i}{13}$

ⓘ A complex number is written in algebraic form a + b*i, a being its real part and b its imaginary part: $\frac{6-17i}{13}$ = $\frac{6}{13}-\frac{17}{13}\times i$

▶Simplified form:   $\frac{6}{13}-\frac{17}{13}\times i$

The numeric value of: $\frac{6}{13}-\frac{17}{13}\times i$ is:

▷ $\approx 0.4615-\approx 1.3077i$