help, idk complex numbers exponential to cartesian form

[noble flame]

i need an answer

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[noble flame]

and an explantion would be nice

Well I'm just guessing

You can use Euler's formula here

$$e^{\theta i} = \cos{\theta} + i\sin{\theta}$$

[ember tapir]

AstroVortex

[noble flame]

And maybe other formulae too

$$\sin{\theta} = -i sinh{i\theta}$$

$$\cos{\theta} = \cosh{i\theta}$$

[ember tapir]

AstroVortex

AstroVortex

[noble flame]

And yeah. Even simpler multiply both sides by $e^{6}$ 'cause you'll be able to use the Lambert W

[ember tapir]

AstroVortex

[noble flame]

So z•e⁶ = $(3+2i)e^{3+2i}$

[ember tapir]

AstroVortex

[noble flame]

Now using Productlog we can simplify it as

$3+2i = W(z.e⁶)$

[ember tapir]

AstroVortex

[noble flame]

Umm probably I'm Overcomplicating it 😐

[noble flame]

i did it

-61.60 and j38.07 is answer

[noble flame]

Now I am become answerer, solver of all questions

https://tenor.com/view/oppenheimer-oppenheimer-movie-walk-walking-gif-3311223081607307352

[queen oyster]

did you realize you are talking to the person who asked the question

[noble flame]

Oh lol

What the-

Sorry @noble flame !