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How do you simplify #20 / (3+i)#?

Answer 1

Serenity Jones

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

#20/(3+i) = 6-2i#

#20/(3+i)#

#= (20(3-i))/((3+i)(3-i))#

#= (20(3-i))/(3^2+1)#

#= (20(3-i))/10#

#=6-2i#

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Answer 2

Serenity Johnson

To simplify ( \frac{20}{3 + i} ), multiply the numerator and denominator by the conjugate of the denominator, which is ( 3 - i ). This process eliminates the imaginary part in the denominator.

[ \frac{20}{3 + i} \times \frac{3 - i}{3 - i} = \frac{20(3 - i)}{(3 + i)(3 - i)} ]

Expand the numerator and the denominator:

Numerator: (20(3 - i) = 60 - 20i)

Denominator: ( (3 + i)(3 - i) = 9 - 3i + 3i - i^2 = 9 + 1 = 10 )

So, after simplifying:

[ \frac{20}{3 + i} = \frac{60 - 20i}{10} = \frac{6 - 2i}{1} = 6 - 2i ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.