SOLUTION: Note: When I use the word "bar" after the complex number expressions, I simply mean there is a bar over each expression. Given z = 3 - 4i and w = 8 + 3i, write each exp

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Note: When I use the word "bar" after the complex number expressions, I simply mean there is a bar over each expression. Given z = 3 - 4i and w = 8 + 3i, write each exp      Log On


   

Question 1208829: Note:

When I use the word "bar" after the complex number expressions, I simply mean there is a bar over each expression.

Given z = 3 - 4i and w = 8 + 3i, write each expression in the standard form
a + bi.

1. z • z bar

2. (z - w) bar



Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given z = 3 - 4i and w = 8 + 3i, write each expression in the standard form
a + bi.
1. z • z bar
2. (z - w) bar
~~~~~~~~~~~~~~~~~~~~~~ 

(1)  z • z bar = (3-4i)*(3+4i) = 3*3 - 4*3i + 4*3i - (4i)*(3i) = 9 - 16*i^2 = 9 - 16*(-1) = 9 + 16 = 25.   ANSWER


     Post solution note :   z* z bar is always real non-negative number (almost always real  positive  number).



(2)  (z - w) = (3-4i) - (8+3i) = (3-8) + (-4i + 3i) = -5 - 7i.

     Therefore  (z - w) bar = (-5 - 7i) bar = -5 + 7i.    ANSWER

Solved.