- Joined
- Feb 16, 2005
- Messages
- 8,375
- Gender
- Male
- HSC
- 2006
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?
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?