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

# Category: Precalculus homework help

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.

Hello,

Original

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.

Hi Everyone

For any given vertical (or horizontal) stretch or shrink, is there a corresponding horizontal (or vertical) stretch or shrink which gives rise to the identical graph transformations? Explain your reasoning. There will always be a corresponding horizontal or vertical stretch or shrink because you will either add or subtract horizontal or vertical which will move the curve right or left depending on what function your using.

Describe a process (step-by-step) in your daily life in which the order of events is important. What would happen if you switched the order? I am used to a routine. Reveille (wake-up call) is usually at 0600. To prepare for the day I rise early at 0430. I get PT (physical training or a workout), showered and about 3 cups of coffee in before 0600. Hence my day starts. Coffee is the most important part of that routine. No coffee equates to a borderline zombie. I am not the friendliest leader or willing to hear any problems until I have had coffee. My day is out of whack without PT and coffee. I seem to get everything under control about 9 or 10ish with them in the mornings.

Describe a process (step-by-step) in your field of study in which the order of events is important. What would happen if you switched the order? Working in the engineering filed there are steps to follow when trouble shooting a piece of equipment from cradle to grave. If for instance the engine will not start, you would not simply add fuel as your first step. You would check your permissive’ s first. (Logics that are put into place to prevent the equipment from starting). Once you have checked these and nothing has been flagged you would move on to the next step of troubleshooting. Going out of order could cause equipment failure and harm to personnel.

A rational function is one that can be written as a polynomial divided by a polynomial or the quotient of polynomials. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. The rational function f(x)= can be transformed using methods similar to those used to transform other types of functions as we saw in last week’s discussion.

The purpose of this week’s discussion is to explore transformations on rational functions using the interactive site Desmos Interactive: Graph of Rational Function Version 2Links to an external site.. Using the interactive site, make adjustments to a, b, c, and d (do at least three transformations/changes).

In your original post, answer the following:

Post screenshots of your three graphs.

Answer the following questions:

How do the variables c and d affect the asymptotes? Which transformation rules were applied?

How do the variables a and b affect the asymptotes? Which transformation rules were applied?

In your opinion, which transformation do you believe is less complicated or easier to understand? Provide justification for your response.

Hi Everyone

For any given vertical (or horizontal) stretch or shrink, is there a corresponding horizontal (or vertical) stretch or shrink which gives rise to the identical graph transformations? Explain your reasoning. There will always be a corresponding horizontal or vertical stretch or shrink because you will either add or subtract horizontal or vertical which will move the curve right or left depending on what function your using.

Describe a process (step-by-step) in your daily life in which the order of events is important. What would happen if you switched the order? I am used to a routine. Reveille (wake-up call) is usually at 0600. To prepare for the day I rise early at 0430. I get PT (physical training or a workout), showered and about 3 cups of coffee in before 0600. Hence my day starts. Coffee is the most important part of that routine. No coffee equates to a borderline zombie. I am not the friendliest leader or willing to hear any problems until I have had coffee. My day is out of whack without PT and coffee. I seem to get everything under control about 9 or 10ish with them in the mornings.

Describe a process (step-by-step) in your field of study in which the order of events is important. What would happen if you switched the order? Working in the engineering filed there are steps to follow when trouble shooting a piece of equipment from cradle to grave. If for instance the engine will not start, you would not simply add fuel as your first step. You would check your permissive’ s first. (Logics that are put into place to prevent the equipment from starting). Once you have checked these and nothing has been flagged you would move on to the next step of troubleshooting. Going out of order could cause equipment failure and harm to personnel.

A rational function is one that can be written as a polynomial divided by a polynomial or the quotient of polynomials. Since polynomials are defined everywhere, the domain of a rational function is the set of all numbers except the zeros of the denominator. The rational function f(x)= can be transformed using methods similar to those used to transform other types of functions as we saw in last week’s discussion.

The purpose of this week’s discussion is to explore transformations on rational functions using the interactive site Desmos Interactive: Graph of Rational Function Version 2Links to an external site.. Using the interactive site, make adjustments to a, b, c, and d (do at least three transformations/changes).

In your original post, answer the following:

Post screenshots of your three graphs.

Answer the following questions:

How do the variables c and d affect the asymptotes? Which transformation rules were applied?

How do the variables a and b affect the asymptotes? Which transformation rules were applied?

In your opinion, which transformation do you believe is less complicated or easier to understand? Provide justification for your response.