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## Main Question or Discussion Point

I'm volunteering in a summer school for year 12 students in my area, and have to teach them a few topics. I've been struggling to get the parametric equations from this.

Sketch: [tex]|z| = \arg(z)[/tex]

So I thought that the obvious way to explain it to them would be to say: "that as the magnitude of z increases (ie. distance from the origin) the greater the angle becomes, thus producing a spiral" and I can draw it on the whiteboard.

Upon attempting the Cartesian equation, I got a bit stuck:

[tex]|z| = \arg(z)[/tex]

[tex]\sqrt{x^2 + y^2} = \tan^{-1}(\frac{y}{x})[/tex]

[tex]\tan{(\sqrt{x^2 + y^2)}}=\frac{y}{x}[/tex]

[tex]y=x\tan{({\sqrt{x^2 + y^2}})}[/tex]

And that is where I get stuck unfortunately. Any thoughts/solutions on how to proceed in finding a Cartesian and/or parametric equations?

(sorry if this doesn't make sense, I haven't done any maths since year 12 haha as I study med atm :/ I miss maths!)

Thanks :)

Sketch: [tex]|z| = \arg(z)[/tex]

So I thought that the obvious way to explain it to them would be to say: "that as the magnitude of z increases (ie. distance from the origin) the greater the angle becomes, thus producing a spiral" and I can draw it on the whiteboard.

Upon attempting the Cartesian equation, I got a bit stuck:

[tex]|z| = \arg(z)[/tex]

[tex]\sqrt{x^2 + y^2} = \tan^{-1}(\frac{y}{x})[/tex]

[tex]\tan{(\sqrt{x^2 + y^2)}}=\frac{y}{x}[/tex]

[tex]y=x\tan{({\sqrt{x^2 + y^2}})}[/tex]

And that is where I get stuck unfortunately. Any thoughts/solutions on how to proceed in finding a Cartesian and/or parametric equations?

(sorry if this doesn't make sense, I haven't done any maths since year 12 haha as I study med atm :/ I miss maths!)

Thanks :)