divide and express the result in standard form.\n$\frac{4}{2 - i}$\n$\frac{4}{2 - i}=\frac{8 + 4i}{5}$…

divide and express the result in standard form.\n$\frac{4}{2 - i}$\n$\frac{4}{2 - i}=\frac{8 + 4i}{5}$ (simplify your answer. type your answer in the form a + bi.)

divide and express the result in standard form.\n$\frac{4}{2 - i}$\n$\frac{4}{2 - i}=\frac{8 + 4i}{5}$ (simplify your answer. type your answer in the form a + bi.)

Answer

Explanation:

Step1: Multiply by conjugate

Multiply numerator and denominator by $2 + i$. We get $\frac{4(2 + i)}{(2 - i)(2 + i)}$.

Step2: Expand expressions

Expand numerator: $4(2 + i)=8 + 4i$. Expand denominator using $(a - b)(a + b)=a^{2}+b^{2}$, so $(2 - i)(2 + i)=2^{2}-i^{2}=4-(-1)=5$.

Step3: Write in standard form

The result is $\frac{8 + 4i}{5}=\frac{8}{5}+\frac{4}{5}i$.

Answer:

$\frac{8}{5}+\frac{4}{5}i$