Complex Numbers in Mod-Arg form (1 Viewer)

[Trebla]

Can someone clarify this to me?:
In an exam, when you convert a complex number x + iy to mod-arg form rcisθ, can you just convert it straight away by using the "Pol(" function on the calculator to find the modulus and the argument, or do you have to show all your working to get the marks?
e.g. when converting z = -1 + i into mod-arg form:
by calculator -
Enter: "Pol(-1, 1)" = √2
"RCL" "tan" = 135
only write: -1 + i = √2.cis135

by using full working - (plus rough diagram)
write:
|z| = √[(-1²) + (1)²]
.: r = √2
In the triangle: (let a be angle created by negative x-axis and modulus)
tan a = 1/1 = 1
.: a = 45
principle argument = θ = 180 - a = 135
.: -1 + i = √2.cis135

Which one of the above would be approved in the exam and by school teachers? I personally like the calculator one because it's quicker, but I don't know if teachers would approve of simply jumping into the conversion instantly.

Also, when a question asks for an argument of a complex number, do we just state the principle argument?
For example, we were just told that the argument of a complex number for something like the above question would be 45º,405º,765º..... and -315º,-675º,-1035º.....
We were told that 45º is only the principle argument since the principle argument is defined as the angle between the positive x-axis and the domain -180<θ≤180.
So when the question asks the argument of a complex number, do we state all values as a general solution or just state the principle argument?

 

[Stefano]

1. Anyway you like; just write the answer down.
2. Principle Argument

 

[Raginsheep]

1. Depends on the mark allocated to the question but I would always do the working. Its not that much extra anyways.
2. Depends on the question but most likely prinicpal argument is fine.

 

[Riviet]

I would show some working to be safe.

 

[Slidey]

You should learn how to do the operations with a normal calculator, as well as recall how to do them in your head in the case of the exact ratios. This way you will be able to work with proofs and shows in the exam, aswell, if they occur.

 

[Trebla]

You are not allowed to bring into the exams calculators which can do complex number operations.

A lot of Board approved calculators have the polar key i.e. Pol(
My calculator is Casio fx-82TL, it must be a Board approved calculator, since I used it in my SC exams. Besides the polar key is the only complex number operation that I know of, which can be done on this calculator anyway as well as many other Board approved calculators.

 

[凍鴛鴦]

The Casio fx-100AU has a Complex Number Mode and is a BOS approved calculator. Note: The AU series is especially designed to meet Australian BOS requirements.

 

[Slidey]

Interesting. I apologise for the misinformation. Is it just graphics calculators that are banned?

 

[Riviet]

Is it just graphics calculators that are banned?

Yes. All of them.
And that reminds me... i was fiddling around with my calc. just before and i found the pol function! Yay, now i can use it to check my arguments

 

[icycloud]

Interesting. I apologise for the misinformation. Is it just graphics calculators that are banned?

There is a guideline for allowable calculators on the Board of Studies site: http://www.boardofstudies.nsw.edu.au/manuals/calculators_hsc_features.html

 

[icycloud]

Yes. All of them.
And that reminds me... i was fiddling around with my calc. just before and i found the pol function! Yay, now i can use it to check my arguments

As well as for complex numbers, I use the Pol function as a quick way to do some trigonometry questions and the Rec function to do Pythagoras.

 

[Trebla]

Back in Year 10, I found the Pol( key and used it for finding the hypotenuse of a right-angled triangle. It wasn't until recently until I discovered the argument on the calculator when I started learning complex numbers. Hmmm, someone tell me what the Rec( function does.....

 

[icycloud]

Back in Year 10, I found the Pol( key and used it for finding the hypotenuse of a right-angled triangle. It wasn't until recently until I discovered the argument on the calculator when I started learning complex numbers. Hmmm, someone tell me what the Rec( function does.....

Pol(x,y) converts Rectangular Coordinates into Polar Coordinates
Rec(r,@) converts Polar Coordinates into Rectangular Coordinates

Rectangular Coordinates are the familiar (x,y) coordinates where x indicates the distance from the y-axis and y indicates the distance from the x-axis

Polar Coordinates on the other hand use r as the distance from the origin and @ as the angle which the line r makes with the x-axis

It just so happens that complex numbers are represented with polar coordinates, but polar coordinates also have many other uses.

Quick example:

Switch to degrees mode,

Rec(2,60) yields x = 1 and y = Sqrt(3)
Pol(1,Sqrt(3)) yields r = 2 and @ = 60