somebody please explin me this or at least give me the correct answer. (complex numbers)

# Somebody please explin me this or at least give me the correct answer

What the fuck does sous la forme mean

Just type that shit in wolframalpha if you want the correct answer. Looks like there would be a "trick" to solve it easily but can't come up with one, though. If not, then it's just a retarded calculation.

@Methshot

From what I remember of the two short years that I took French in high school it means "in the form"

@idontknow

It has 14 solutions and doesn't state in which branch you need to provide the answer. What a piece of literal shit.

Convert it into polar form and then just do r^14 and 14*arg. Then convert it back to rectangular form.

@StrangeWizard

Shit you're right, I'm a bit drunk...

Anyway OP, just use Yooler, then De Moivre's formula.

convert to polar form

apply de moivre's theorem

kys

@Raving_Cute

apply de moivre's theorem

Nonsense! De Moivre was a crank who believed in "transcendental functions". Sine and cosine do not exist. THEY ARE SPOOKS.

You can clearly work this problem out in [math] \mathbb{Q} (i, \sqrt{3}) [/math] and apply the beautiful and elegant binomial theorem! It would be nonsense to use "real numbers" to solve this problem when you can simply use real mathematics that actually exists in the real world.

@idontknow

(3(-1/2+i√3/2))^14

(3(cos(150°)+i*sin(150°))^14

(3∠150°)^14

3^14∠150°*14

3^14∠300°

3^14(1/2-i√3/2)

QED

@idontknow

[math] \frac{3}{2} ( \sqrt{3} i -1 ) = 3 ( \frac{\sqrt{3}}{2} +i (-\frac{1}{2}) ) =3( \cos{\frac{-\pi}{6}} + \sin{\frac{-\pi}{6}} ) = 3 e^{-i \frac{\pi}{6}} \implies (\frac{3}{2} ( \sqrt{3} i -1 ) )^{14} = 3^{14} e^{-i \frac{14\pi}{6}} =3^{14} e^{-i \frac{\pi}{3}} = 3^{14} (\frac{1}{2} - i \frac{\sqrt{3}}{2}) [/math]

@SomethingNew

Oh, I'll call you. I will call you to tell you that I'm proud for actually finding the solutions rigorously.

@Poker_Star

[math] \pi [/math]

I am sorry, but what is this weird symbol I see here. Is this a number? Can you please write it down so I may see its digits?

@Carnalpleasure

Oh, then I must have misjudged you. It is a beautiful symbol for 3 indeed. Very classic. It can be drawn with 3 strokes precisely. Clever.

That said, we are not done examining your "proof".

sin

cos

I am sorry but what are these? Can you please write down the expression that gives the value for these functions? I have never seen these. Are you sure they exist?

I can't LaTeX to work on Veeky Forums today, but here you go.