SOLUTION: Hello... I am having some trouble with a proof. I am to use: (a + bi)(a - bi) The problem asks: Show that for a + bi not equal to 0 this product is a positive real num

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Hello... I am having some trouble with a proof. I am to use: (a + bi)(a - bi) The problem asks: Show that for a + bi not equal to 0 this product is a positive real num      Log On


   

Question 4786: Hello...
I am having some trouble with a proof. I am to use:
(a + bi)(a - bi)
The problem asks:
Show that for a + bi not equal to 0 this product is a positive real number.
Thanks for your help.

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
The question is wrong. there are values of a and b that make the above product a non positive (zero) number. However, the product is always non-negative (non-negative numbers include positive numbers and zero).
Proving it it is very easy.

sub of two squares a%5E2%2Bb%5E2 is always non-negative.