SOLUTION: Find the absolute value. 1.) |3-i| 2.) |-2+3i|

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find the absolute value. 1.) |3-i| 2.) |-2+3i|      Log On


   

Question 175628: Find the absolute value.
1.) |3-i|
2.) |-2+3i|
Found 2 solutions by EMStelley, jim_thompson5910:
Answer by EMStelley(208) About Me  (Show Source):
You can put this solution on YOUR website!
If z = a+bi, then
abs%28z%29=sqrt%28a%5E2%2Bb%5E2%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1)

Since 3-i is in a%2Bbi form, we can see that a=3 and b=-1


abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29 Start with the absolute value of a complex number formula.


abs%283-i%29=sqrt%28%283%29%5E2%2B%28-1%29%5E2%29 Plug in a=3 and b=-1.


abs%283-i%29=sqrt%289%2B%28-1%29%5E2%29 Square 3 to get 9.


abs%283-i%29=sqrt%289%2B1%29 Square -1 to get 1.


abs%283-i%29=sqrt%2810%29 Add.


abs%283-i%29=3.162 Approximate (this step may be optional)







2)

Since -2%2B3i is in a%2Bbi form, we can see that a=-2 and b=3


abs%28a%2Bbi%29=sqrt%28a%5E2%2Bb%5E2%29 Start with the absolute value of a complex number formula.


abs%28-2%2B3i%29=sqrt%28%28-2%29%5E2%2B%283%29%5E2%29 Plug in a=-2 and b=3.


abs%28-2%2B3i%29=sqrt%284%2B%283%29%5E2%29 Square -2 to get 4.


abs%28-2%2B3i%29=sqrt%284%2B9%29 Square 3 to get 9.


abs%28-2%2B3i%29=sqrt%2813%29 Add.


abs%28-2%2B3i%29=3.606 Approximate