Do you  think that the matrices we introduced in this discussion are good  sta

 
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

 
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.

  Polar Form and Rectangular Form Notation for Complex Numbers. (n.d.). All Abou

 
Polar Form and Rectangular Form Notation for Complex Numbers. (n.d.). All About Circuits. https://www.allaboutcircuits.com/textbook/alternating-current/chpt-2/polar-rectangular-notation/Links to an external site. Rectangular notation  denotes a complex number in terms of its horizontal and vertical  dimensions. So 4+J4 could also be said as 4 Right and 4 up on a graph.  The first 4 is your real number and the J4 is the imaginary number. I  liked this website because it walks through the basics and builds on  that, for both polar form and rectangular form. 
Johnson, L. (2019, March 2). How to Use a Coordinate Plane in Real Life. Sciencing. https://sciencing.com/use-coordinate-plane-real-life-8743000.htmlLinks to an external site.  I like this site because it gives real world examples of how these  numbers are used. Calculating waveforms in AC electricity is the first  example that stood out to me as something that I could actually  understand.   

  will be discussing websites that help explain Rectangular and Polar Form of co

 
will be discussing websites that help explain Rectangular and Polar Form of complex numbers.
Polar and Rectangular Notations and Conversions. (Electrical Engineering, n.d.). www.electricalengineering.xyzLinks to an external site. . The  Ultimate Guide to Polar and Rectangular Notations and Conversions  Everyone doing Electrical Should know (electricalengineering.xyz)Links to an external site.
I  liked this website because it was easy to understand, and it has  examples of both form of complex numbers. It describes rectangular form  as a complex number denoted by its respective horizontal and vertical  component. The horizontal component is your real number, and the  vertical component is your imaginary number. Polar form is a complex  number denoted by the length (magnitude, absolute value) and the angle. 
Complex Number Forms. (Academy, 2022) www.khanacademy.orgLinks to an external site.. Complex number forms review (article) | Khan AcademyLinks to an external site.  -This website describes rectangular and polar forms. It provides  formulas and it shows how to convert rectangular form to polar form and  vice versa. This site also includes visuals and examples.  Another we  will discuss will be exponential form which uses the same system as  polar form.
Another tool to assist with understanding complex numbers:
Polar & rectangular forms of complex numbers (video) | Khan AcademyLinks to an external site.
References
Academy, K. (2022). Khan Academy. Retrieved from Complex  Number Forms:  https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-polar/a/complex-number-forms-review
BYJU’S. (2022). byjus.com. Retrieved from Math/Complex numbers: https://byjus.com/maths/complex-numbers/
Electrical Engineering. (n.d.). Retrieved from Polar and  Retangular Notations and Conversions:  https://www.electricalengineering.xyz/article/polar-and-rectangular-notations-and-conversions/
Flylib.com. (2020). Retrieved from The Notation of complex numbers: https://flylib.com/books/en/2.729.1/the_notation_of_complex_numbers.htmlLinks to an external site.
a +bi = 3+4i Example plotted below
How would you plot -2+2i

  I  chose the Pythagorean Theorem for my topic this week. Pythagorean  theorem

 
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
1002=10,000
10,000+10,000=20,000
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?
References
Merriam-Webster. (n.d.). Pythagorean theorem. In Merriam-Webster.com dictionary. Retrieved August 10, 2022, from https://www.merriam-webster.com/dictionary/Pythagorean%20theorem