Euler formula Definition and 14 Threads

Euler gave us the below equations: But this doesn't actually give me a number value for where the y value is when you plug in a number for x. For example, if i plug in 2pi for x, i know cosx should be 1. But that equation gives me (e^2i*pi +e^-2i*pi)/2. This doesn't give me 1. So what really...

Hello, This is actually not homework. I was google searching for "proving trig identities from geometric point of view), found one of the result which proves trig identities using Euler formula. I really liked it. Easier, quicker & simple. But when the author speak about sum to product formulas...

I differentiated both sides of Euler's formula with respect to x : e^ix = sin x + i cos x => ie^ix = cos x - i sin x Then for comparison I multiplied both sides of Euler's formula by i: e^ix = sin x + i cos x => ie^ix = i sin x - cos x Each of these two procedures seems to yield the...

Hello, I am enrolled in calculus 2. Just having started a section in our textbook about integration by partial fractions, I eagerly began trying to use this integration technique wherever I could. After messing around for multiple days, I ran into this problem: ∫ 1/(x^2+1)dx I immediately...

Can anyone provide me with a simple explanation for why e^i(x) acts like this.

can someone explain how you go from (4.25) to (4.26) using Euler's formulas in the attachment?

For Euler formula : e(iπ) + 1 =0 is it the same if we say e(-iπ)+1 = 0 or not ? (minus sign is included in the exponent)

when I am using Euler equation for Fourier transform integrals of type \int_{-\infty}^{\infty} dx f(x) exp[ikx] I am getting following integrals: \int_{-\infty}^{\infty} dx f(x) cos(kx) (for the real part) and i* \int_{-\infty}^{\infty} dx f(x) sin(kx) (for its imaginary part) I am...

Homework Statement I have a code that successfully plots the trajectory of a ball moving under gravity and air resistance, but my method is rather long-winded and I want to use a 4d vector-first order ODE instead - but I don't know how to do it. I've tried writing some simple skeletons but...

why is psi = cos (k r - w t) + i sin ( k r - w t) = e^ [ i ( k r - w t)]? my question precisely is why not: 1. psi = sin (k r - w t) + i cos ( k r - w t) ? 2. psi = sin (k r - w t) + i sin ( k r - w t) ? 3. psi = cos (k r - w t) + i cos ( k r - w t) ? why not any of these three? is...

Homework Statement Since the exercise has a graph I uploded it here :http://imageshack.us/photo/my-images/833/img9845wz.jpg/ fmax(t)=1 T=2Pi h=1,3,5,7,... Also I was told that I could use Eulers formula here. Homework Equations maybe someone could give me some tips how to make the...

I'm reading a book called The Road to Reality by Roger Penrose, and I'm on the chapter for complex logarithms. What I don't understand is how the identity e\theta i = cos \theta + i sin \theta is found through the use of complex logarithms. I also don't understand how if w = ez, z = log r +...

Is it possible to prove Euler's identity (e^i*pi = -1) without simply taking it as a special case of Euler's formula (e^i*x = cos(x) + i sin(x))?