complex numbers

[keen kernel]

Determine all complex numbers (picture).
Provide the solutions in the form (picture).

Please help me. Idk how to start. I have to teach everything myself. The only thing i know is that i is sqrt(-1)

[paper axle]

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[fickle venture]

Suppose we have z^n = w, and also r = |w| and θ = arg(w). Then the solutions of this equation are:
z = r^(1/n) e^(θ + 2πik/n), k = 0, ..., n - 1

[vernal haven]

look for De Moivre theorem

[honest vortex]

1/i= 1/i x i/i that might help

[vernal haven]

$$ \frac{1}{i} = -i = \exp(i\frac{3\pi}{2}) $$

[tribal chasm]

aL

[vernal haven]

rest should be easy

@keen kernel

[keen kernel]

need a moment to process everything

[vernal haven]

[keen kernel]

haha

[keen kernel]

okay I literally understand anything

[keen kernel]

thats -i I guess yeah

[honest vortex]

good job

[keen kernel]

my bad

dont*

lmao

[meager hinge]

@keen kernel

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[keen kernel]

I will jump of a bridge

Hope the Media wont say there werent any evidence

[waxen schooner]

no jumping off a bridge, that's against the server rules

[keen kernel]

[wispy sapphire]

maybe try rewriting z^3 as r(cos3v+isin3v) on the lhs and rewrite 1/i in a similar form

equate

like aL said its de moivres theorem for roots of unity

[fickle venture]

Exponential form is better here.

[wispy sapphire]

both work ig

[fickle venture]

That's how this formula is derived.

[wispy sapphire]

yea