Choice of notation kinda (complex numbers)

[sharp shard]

So im doing this problem where you write the function sin to the power of 6 (theta) in terms of just cos thetas that could be times by constants like cos(4 theta). The textbook uses the method of expressing z = cos(theta) + isin(theta) and then expanding out (z - 1/z)^6 and then equating the terms but i expand it out like (e ^i theta - e^i (-theta))^6 im sorry i didnt use the theta symbol btw. Which one should I do?

[hollow gorge]

Can u show the question

Instead of text

Also show ur work

[brazen trout]

z=e^iθ and 1/z =e^-iθ, it's just a shorthand of what it sounds like you're doing

You can expand (e^iθ+1/e^iθ)^6 and end up with the same result, but since e^iθ is ANY complex number then a shorthand to write any complex number is also just z, z=e^iθ

[brazen trout]

The question is about notation I'm not really sure if showing work would do much

[hollow gorge]

I wanted to see his work

Whether he has really tried

[brazen trout]

I mean given what they said the method sounds correct, they just aren't sure about the textbook's notation of z and 1/z

Unless their work is different to what they said in the description it shouldn't matter here since it's a reading/notation issue rather than an actual problem solving issue

[sharp shard]

Yeah i know how to do the question

I was just wondering

If i should focus on doing the shorthand z method or js do the e^i theta

Because i feel more comfortable js doing the e^itheta way but it does make the working out look cleaner by equating that to z

but then the relations dont feel as intuitive as z + 1/z = 2i sin(theta)

compared to e ^ (-i theta) + e^ (itheta) feels alot more natural cause i can see it as cos and sin instead of a variable

[brazen trout]

I think for (z+1/z)^2 or something it won't matter but when you have to do like (z+1/z)^6 or like a pretty big power it will take too much time to write out e^iθ