+0  
 
0
76
1
avatar

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

Guest Jan 17, 2018
Sort: 

1+0 Answers

 #1
avatar
0

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

 

 

 

 

 

Guest Jan 17, 2018

12 Online Users

avatar
avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details