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.

Step-by-step 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

the answer is b.)

< 1=< 2

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;