1.find the complex conjugate of -14+11i a. -14-11i b. 14-11i c. 14+11i d.11+14i 2.simplify the expression ( sqrt 3+i)( sqrt 3-i) a.2 b.2i c. sqrt3+i d.4

1. The conjugate of a complex constant is what we get when we change i to -i.

The conjugate of -14 + 11 i is simply

-14 - 11 i choice A

2. The product of complex conjugates is the squared magnitude, which is the sum of squares of the real part and the imaginary part. It will always be real.

Let's work it out a few ways. FOIL first:

Now just as the sum of squares of the real part and the imaginary part:

Choice D

answer: it's d

step-by-step explanation:

unless you made a typo, the answers are both a and c.

step-by-step explanation:

1.5/3 is .5 whereas 3/9 is .3333333 not proportional

22/33 is .66666 and 4/6 is also .66666 proportional

2/4 is .5 whereas 142/213 is .66666 not proportional

14/7 is 2 and 7/3.5 is also 2 proportional

you could've also checked it by doing this simple division:

if the larger fraction divides with the smaller fraction to equal 1, it is proportional. so let me show you what i mean:

when i divide 22/33 by 4/6 i get 1, so we know it is proportional, and it is the same with 14/7 and 7/3.5. now if i divide 3/9 by 1.5/3 i get .66666 so therefore we know it is not proportional.

there are many ways to do this so i wanted to show you some possible ways.