Trigonometric form of a complex number

[Loki123]

Excuse me if I am in the wrong topic, I am not sure where this goes.

So I have a complex number z=-2+6i and I am supposed to find its trigonometric form. I am supposed to get that alpha equals 108 degrees, how? Without a calculator if possible.

 

[topsquark]

Actually $\alpha \approx 108.4 ^o$. You can't do that without the calculator, though.

-Dan

 

[The Highlander]

Excuse me if I am in the wrong topic, I am not sure where this goes.

So I have a complex number z=-2+6i and I am supposed to find its trigonometric form. I am supposed to get that alpha equals 108 degrees, how? Without a calculator if possible.

Hi Loki,

Maybe have a look here & here?

Calculator (here) gives:-

z = 6.3246 (cos (108.4349) + sin (108.4349) i)
z = 6.3246 ((-0.3638) + (0.9315) i)
z = -2.3009 + 5.8914 i​

Do any of those match up with your book's answer?

 

[The Highlander]

Excuse me if I am in the wrong topic, I am not sure where this goes.

So I have a complex number z=-2+6i and I am supposed to find its trigonometric form. I am supposed to get that alpha equals 108 degrees, how? Without a calculator if possible.

Does the question specifically state that you must determine the value of α without the use of a calculator?
Can we see this, please?
If no calculated (approximated) value for α is to be used then the only way I can see to complete the conversion to trig. form is to express it thus:-

z = 2√10(cos(ᴨ+tan^-1(-3)) + i sin(cos(ᴨ+tan^-1(-3)))​

How does that compare to your "book's" answer?

 

[Loki123]

Does the question specifically state that you must determine the value of α without the use of a calculator?
Can we see this, please?
If no calculated (approximated) value for α is to be used then the only way I can see to complete the conversion to trig. form is to express it thus:-

z = 2√10(cos(ᴨ+tan^-1(-3)) + i sin(cos(ᴨ+tan^-1(-3)))​

How does that compare to your "book's" answer?

It's not about the "book" stating it, it's just genuine curiosity. The book is just a term I use to differentiate between my solution and the original.