simplify 4/(5-2i) — step-by-step solution

Let's simplify:

\frac{4}{5 - 2 i}

ⓘ To make the denominator real, multiply the numerator and denominator by its conjugate, since (a+bi)(a-bi) = a²+b²:

\frac{4}{5 - 2 i}

\frac{4 \times (5 + 2 i)}{5^{2} + {(-2)}^{2}}

\frac{4 \times (5 + 2 i)}{5^{2} + {(-2)}^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

5^{2}

5 \times 5

25

{(-2)}^{2}

(-2) \times (-2)

4

\frac{4 \times (5 + 2 i)}{25 + 4}

ⓘ The numerator and the denominator are computed before the division:

25 + 4

29

\frac{4 \times (5 + 2 i)}{29}

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

\frac{4 \times (5 + 2 i)}{29}

\frac{20}{29} + \frac{8}{29} \times i

▶Simplified form:

\frac{20}{29} + \frac{8}{29} \times i

The numeric value of:

\frac{20}{29} + \frac{8}{29} \times i

equals:

▷

\approx 0.6897 + \approx 0.2759 i