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Compute $|5-12i| + |3-4i|$.

 Jan 17, 2018
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Simplify the following:

abs(-12 i + 5) + abs(-4 i + 3)

 

Absolute value gives the distance to the origin.

abs(5 - 12 i) = sqrt(Re(5 - 12 i)^2 + Im(5 - 12 i)^2) = sqrt(5^2 + (-12)^2):

sqrt(5^2 + (-12)^2) + abs(3 - 4 i)

 

sqrt(25 + (-12)^2) + abs(3 - 4 i)

 

sqrt(144 + 25) + abs(3 - 4 i)

 

sqrt(169) + abs(3 - 4 i)

 

Simplify radicals.

sqrt(169) = sqrt(13^2) = 13:

13 + abs(3 - 4 i)

 

Absolute value gives the distance to the origin.

abs(3 - 4 i) = sqrt(Re(3 - 4 i)^2 + Im(3 - 4 i)^2) = sqrt(3^2 + (-4)^2):

sqrt(3^2 + (-4)^2) + 13

 

sqrt(9 + (-4)^2) + 13 = 18

 

 

 

 

 

 Jan 17, 2018

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