How do you simplify $\frac{5}{2 - i}$ $5/(2-i)$ ?

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How do you simplify $\frac{5}{2 - i}$ $5/(2-i)$ ?

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Answer 1 · 2018-08-07T00:08:23

$2 + i$ $2+i$

Explanation:

$\frac{5}{2 - i}$ $5/(2-i)$

Multiply numerator and denominator by the denominator's conjugate:
$= \frac{5}{2 - i} \cdot \frac{2 + i}{2 + i}$ $=5/(2-i) color(blue)(* (2+i)/(2+i))$

Simplify:
$= \frac{10 + 5 i}{4 - i^{2}}$ $=(10+5i)/(4-i^2)$

$= \frac{10 + 5 i}{4 + 1}$ $=(10+5i)/(4+1)$

$= \frac{10 + 5 i}{5}$ $=(10+5i)/5$

$= 2 + i$ $=2+i$

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How do you simplify $\frac{5}{2 - i}$ $5/(2-i)$ ?

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