Do you think that the matrices we introduced in this discussion are good stand-ins for complex numbers? Explain your reasoning. Is there any operation/task where they might fail to “impersonate” complex numbers?
To me matrices are usually harder to solve than doing the work for complex numbers. It’s a different way of thinking about the numbers than I am used to, and adds more “rules” to remember.
If all you needed to do with complex numbers was add them, which format would you choose to use? Briefly explain.
If all you needed to do with complex numbers was multiply them, which format would you choose to use? Briefly explain.
If you needed to add, multiply, and find magnitudes for complex numbers which format would you choose to use? Briefly explain.
For all three questions above I would rather use rectangular form as of right now. Complex numbers are added/multiplied the same as any other algebra problem, as long as you keep in mind if a i2 comes up its no longer representing an imaginary number, but -1, you can do the math the same as if it had an x instead of an i.
Image attached with numbers shown.
Using the rectangular form seems like it is the simplest out of the three forms. It’s very easy to understand and does not come with as many steps.
Personally, I think matrices can be a good stand in for complex numbers. The only problem I would see occurring is when multiplying, due to the chance of the matrices not being the same size.
I chose the Pythagorean Theorem for my topic this week. Pythagorean theorem states that “the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides.” (Merriam-Webster.com). Another way of saying this is A2+B2=C2
So lets say I’m getting ready to build a fence around a bit of land that is 100′ by 100′
but I don’t need the fence to go around all four sides, instead I need it to go down two sides, and then the shortest distance back to the first fence. (marked in red)
How much fence material would I actually need?
Since I know that A2+B2=C2, I know that 1002+1002=?2
Then you have to take the square root of 20,000, which is ~141.42. So I would need 141.42′ of fencing to cover the middle section (hypotenuse) of the field. I would need to add 141.42’+100’+100=341.41′ of fencing would be needed to cover the area I want to cover.
For the problem I’m supposed to give the class to solve Ill ask what is the distance between first base, and third base on a baseball field which is a 90’x90′ square?
Merriam-Webster. (n.d.). Pythagorean theorem. In Merriam-Webster.com dictionary. Retrieved August 10, 2022, from https://www.merriam-webster.com/dictionary/Pythagorean%20theorem
I researched Reference and Conterminal angels.
Conterminal angels are angles with the same initial and terminal sides. However, the rotations could be different hence the co-terminal.
Reference angel is the smallest positive acute angle formed by terminal side of the angle t and horizontal x axis. (Blitzer, 2021)
Find the Reference angle of the following : I will find by adding or subtracting 360 from the given angle ,
Find the Conterminal angle of the following : I will find by adding and or subtracting
, first you need a common denominator to add or subtract.
Find the following refence and conterminal angels:
Blitzer, R. F. (2021). Precalculus (7th Edition). Pearson Education (US).
moved a to positive 0.9-Right upper left quad shrank or shifted down below the x axis. The lower right quad moved from above the x axis to below the x axis.
moved b to negative 1.3 – Horizontal flips Shifts the upper left quad to the right and the bottom right quad to the left.
Moved c to positive 2.7 ( horizontal flip – i think is the right term but the graphs got shorter)
Moved d to positive 1-flidped vertically both quads and they shifted up
I don’t know that I have one that was easier than the other but if I had to make a choice. I would chose moving d to a positive because you can clearly see that the graphs were flipped vertically and shifted up higher. I could be wrong as I am still having trouble with functions.
How do the variables c and d affect the asymptotes? Which transformation rules were applied?
In the graph below I changed the C=6 and kept D=-.2 / A=-3.6 / B=3.3
The asymptotes shifted down as a result to increasing C. Also, the transformation flipped.
In the graph below I changed the D=6 and kept C=-1 / A=-3.6 / B=3.3
The asymptotes shifted to the right as a result to increasing D. Also, the transformation did flip.
How do the variables a and b affect the asymptotes? Which transformation rules were applied?
In the graph below I changed the A=6 and kept C=-.1 / D=-.2 / B=3.3
The asymptotes shifted down as a result to increasing a. Also, the transformation did not flip.
In the graph below I changed the B=8 and kept C=-1 / D=-.2 / A=-3.6
The lines graphed here widened as a result to the increase in B.
In your opinion, which transformation do you believe is less complicated or easier to understand? Provide justification for your response.
I believe the x=-D/C is the easiest for me to understand with adjusting the Variables (D, C). For instance, when I changed D=6 the equation for the X coordinate was because, 6/1=6.