Question

For this problem we will use the complex numbers 3 - 6i and 9 + i

What is the conjugate of each complex number?



What is the sum of the complex numbers? Show all work.



What is the sum of the conjugates of the complex numbers? Show all work.



How does the sum of the conjugates compare to the sum of the original complex numbers? Explain.

Answer 1

Explanation:

conjugates are the the same number with an opposite sign in the middle

3 - 6i = 3 + 6i ' the ' mark often denotes a conjugate.. and other things

9 + i = 9 - i '

because complex number represent two different ..(orthogonal ) directions... or at a right angle.. they don't affect each other at all

so to add we just add those part independently

A) (3 - 6i ) + (9 +i )

3+9 + (-6+1)i = 12-5i

B) ( 3 + 6i) + ( 9 - i)

(3+9) + (6+ (-1)) i

12 +5i

C) notice the only difference of the sum of the conjugates is the sign, and so the sum of the conjugates is itself a conjugate too :) this is handy .. especially in elect. engineering :P