How do you simplify $\frac{20}{3 + i}$ $20 / (3+i)$ ?

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How do you simplify $\frac{20}{3 + i}$ $20 / (3+i)$ ?

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Answer 1 · 2015-12-16T00:43:52

Multiply both numerator and denominator by the Complex conjugate $(3 - i)$ $(3-i)$ of the denominator and simplify to find:

$\frac{20}{3 + i} = 6 - 2 i$ $20/(3+i) = 6-2i$

Explanation:

$\frac{20}{3 + i}$ $20/(3+i)$

$= \frac{20 (3 - i)}{(3 + i) (3 - i)}$ $= (20(3-i))/((3+i)(3-i))$

$= \frac{20 (3 - i)}{3^{2} + 1}$ $= (20(3-i))/(3^2+1)$

$= \frac{20 (3 - i)}{10}$ $= (20(3-i))/10$

$= 6 - 2 i$ $=6-2i$

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How do you simplify $\frac{20}{3 + i}$ $20 / (3+i)$ ?

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