How is exp(i*Pi/4) related to (1+i)/sqrt2?

  • Thread starter Thread starter Chronos000
  • Start date Start date
  • Tags Tags
    Exponential
Chronos000
Messages
80
Reaction score
0

Homework Statement



I need to use the relation exp(i*Pi/4) = (1+i)/sqrt2 but I'd like to know where it came from. I am clueless about how to arrive at this.
 
Physics news on Phys.org
What you're looking for is this identity:
e^{i x} = cos(x) + i sin(x)
 
ah, so simple, thanks
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
View full post »

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Fourier Transform - Solutions Error?
Replies
5
Views
1K
Prove that the integral is equal to ##\pi^2/8##
2
Replies
98
Views
4K
Reduced equation of quadratic forms
Replies
1
Views
2K
Checking convergence of Gaussian integrals
Replies
47
Views
4K
How to prove rational sequence converges to irrational number
Replies
2
Views
2K
Evaluating Cartesian integral in polar coordinates
Replies
11
Views
2K
Setting up an integral (Spherical Coordinates)
Replies
1
Views
1K
How can the recurrence formula for a sequence be found?
Replies
3
Views
1K
How do I evaluate this integral?
Replies
6
Views
1K
How Do You Find the Gradient Vector from a Directional Derivative?
Replies
5
Views
1K

Hot Threads

Recent Insights

Back
Top