2 Answers

IsADon · Answer 1 · 2021-06-18T03:37:13+0000

Answer:

$\boxed{\sf B) \ 2-i}$

Explanation:

$\sf (2+i)/(5)$

Reciprocal the fraction.

Switch the denominator with the numerator.

$\sf (5)/(2+i )$

Multiply the numerator and the denominator with the conjugate
$\sf 2-i$ .

$\sf (5(2-i))/((2+i)(2-i))$

$\sf (10-5i)/((2+i)(2-i))$

Apply rule to solve for the denominator:

$\sf (a+bi)(a-bi)=a^2 +b^2$

$\sf a=2\\b=1$

$\sf (10-5i)/(2^2 +1^2 )$

$\sf (10-5i)/(4+1)$

$\sf (10-5i)/(5)$

Simplify the fraction.

$\sf (10)/(5)-(5i)/(5)$

$\sf 2-i$

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