multiplying argand diagrams

[brittle knoll]

im just confused

[ionic reef]

still need explanation

[brittle knoll]

yes please

[grand rivet]

using de moivre's

you know that (cos4t + isin4t) = (cost + isint)^4

and (cos(-t) + isin(-t)) = (cost + isint)^-1

so (cost + isint)^4 * (cost + isint)^-1 = (cost + isint)^3 = cos3t + isin3t

[brittle knoll]

what is de moivre?

[long crow]

This is year 13 content if you’re doing edexcel

[brittle knoll]

just use year 12 knowledge to explain to me

[long crow]

Okay so
If you have a complex number z in the form $$z = r\left(cos(\theta) + isin(\theta)\right)$$
Then $$z^n = r^{n} \left(cos(n\theta) + isin(n\theta)\right)$$

[stray sun]

secp256k1

[long crow]

And the part before wasnt explained either

but there are odd / even functions right

You always want the arguments of each complex number to be the same and the complex number to also be in the form cosθ + isinθ

[brittle knoll]

??

sorry I didn't reply, I slept

[ionic reef]

u dont rlly need demoivres

when u multiply 2 complex numbers, u need to know that u hv to add their arguments

but the second one isnt in modulus-argument form because there is a minus between the cos and isin

so they rewrote it

thus, the arguments were 4theya and -theta

and added together to get 3theta

[brittle knoll]

yeah I realised

I panicked when you said de moivres