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Difference, parametric vs rectangular vs polar equations?

To give you an idea of how much I know/dont know, I think this has something to do with trig identities and imaginary numbers. Can you tell me what I need to know in order to understand this?
Basic definitions please?
Edits: No where seems to give a straight up definition they just talk about them.
Examples would be great I'm freaking STUCK
(edited 3 years ago)
Reply 1
Original post by NeedABtterUserID
To give you an idea of how much I know/dont know, I think this has something to do with trig identities and imaginary numbers. Can you tell me what I need to know in order to understand this?
Basic definitions please?
Edits: No where seems to give a straight up definition they just talk about them.
Examples would be great I'm freaking STUCK

Before saying anything that would be unhelpful, I want to make sure I understand what you are asking. Are you asking why would we bother using three different ways of looking at the same equation? Or is it a more technical question about what the different equations are and how to use them?
Original post by Pangol
Before saying anything that would be unhelpful, I want to make sure I understand what you are asking. Are you asking why would we bother using three different ways of looking at the same equation? Or is it a more technical question about what the different equations are and how to use them?

I mean, both?

The complex numbers z and w are given by z = 2 j and w = 1 + 5j.
(a) Calculate
(z^2 + w)/(1 z)
.
(b) Convert your answer to part (a) into polar form.


Like what form is it in? I looked it up and found about other forms and was just confused. What does polar form look like?
(edited 3 years ago)
Original post by NeedABtterUserID
I mean, both?

The complex numbers z and w are given by z = 2 j and w = 1 + 5j.
(a) Calculate
(z^2 + w)/(1 z)
.
(b) Convert your answer to part (a) into polar form.


Like what form is it in? I looked it up and found about other forms and was just confused

Polar form is where you express a coordinate in terms of the distance from the origin to it (known as the radius) and the angle at which it is measured anticlockwise from the positive horizontal axis (known as the argument)

The polar form of a complex number z=x+iyz = x + i y is just z=R(cosθ+isinθ) z = R (\cos \theta + i \sin \theta) where RR is the radius and θ\theta is the argument.
Original post by RDKGames
Polar form is where you express a coordinate in terms of the distance from the origin to it (known as the radius) and the angle at which it is measured anticlockwise from the positive horizontal axis (known as the argument)

The polar form of a complex number z=x+iyz = x + i y is just z=R(cosθ+isinθ) z = R (\cos \theta + i \sin \theta) where RR is the radius and θ\theta is the argument.

Oh dear, why isn't that just one angle with a magnitude, why does it have a cos and sin component surely its just a 2D graph with a line hence angle and magnitude, or is it height + width where R is the magnitude? I think I dont understand compound angles?
Original post by NeedABtterUserID
Oh dear, why isn't that just one angle with a magnitude, why does it have a cos and sin component surely its just a 2D graph with a line hence angle and magnitude, or is it height + width where R is the magnitude? I think I dont understand compound angles?

sine and cosine are what allows you to decompose into the real and imaginary components respectively for a given complex number.

So the real component is x=Rcosθx = R\cos \theta and the imaginary component is y=Rsinθy = R\sin \theta. Just basic trigonometry once you look at it as a line on a 2D graph.
Reply 6
Original post by NeedABtterUserID
I mean, both?

The complex numbers z and w are given by z = 2 j and w = 1 + 5j.
(a) Calculate
(z^2 + w)/(1 z)
.
(b) Convert your answer to part (a) into polar form.


Like what form is it in? I looked it up and found about other forms and was just confused

This question isn't about equations. You are just being asked to find some complex numbers, and express them either in x + iy form (which you could call rectangular if you like, although it's a bit odd to use that terminology here) or in polar form, which as @RDKGames says involves saying how far away they are from the origin and what angle you would have to turn through to look at them (relative to the positive x-axis, or positive real axis).

I expect you can find them in x + iy form without any trouble (apologies if not, let us know and I'm sure we can help). You then have to convert them into polar form, which is fairly easily done using r2 = x2 + y2 and tan θ = y/x (although you need to give a bit of thought as to what quadrant they are in).

I expect the problem is that you are just meeting this for the first time and are doing this without having had an explanation as to why you would bother. All I can say at this point is that you will meet many problems involving complex numbers which are far easier to tackle when using polar form rather than x + iy form.

Parametric doesn't really come in to this, unless you have an example you can show us that mentions it.

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