SOLUTION: Let z=-8+15i and w=6-8i. Compute (zz\bar)/(ww\bar) where the bar represents the complex conjugate.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: Let z=-8+15i and w=6-8i. Compute (zz\bar)/(ww\bar) where the bar represents the complex conjugate.       Log On


   

Question 1085380: Let z=-8+15i and w=6-8i. Compute (zz\bar)/(ww\bar) where the bar represents the complex conjugate.
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
.
If z = a + bi is any complex number,  then z_bar = a - bi,  and 


z*z_bar = a%5E2+%2B+b%5E2.



For the given numbers, z*z_bar = 8%5E2+%2B+15%5E2 = 64 + 225 = 289,

                  and  w*w_bar = 6%5E2%2B8%5E2 = 36 + 64 = 100.

See introductory lessons on complex numbers
    - Complex numbers and arithmetical operations on them
    - Complex plane
    - Addition and subtraction of complex numbers in complex plane
    - Multiplication and division of complex numbers in complex plane
in this site.


Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Complex numbers".



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





Conjugates:





Using those four pieces of info, we know that,