# Can you prove DeMoivre's theorem

The sentence by Moivre Andreas Pester University of Applied Sciences K rnten, Villach

[email protected]

One would also have the example using the binomial formula for (

e

[email protected]

**Summary**: Brief derivation of Moivre's theorem and its application to the exponentiation of complex numbers. Main page**Keywords**: Moivre's theorem | Raising complex numbers to the power of | The complex power function | Equation 1 | Equation 2 | Example 1 | Example 2 The following theorem for integer exponents n follows from Euler's formula according to the laws of power calculation: because it applies If one applies theorem (1) to any complex number*z*= |*z*| · E^{i · f}on, that's how you get the formula for raising complex numbers to the power.**Example 1:**One would also have the example using the binomial formula for (

*a*+*b*)^{n}can solve, but with increasing power and for non-integer real and imaginary parts, the numerical effort becomes relatively high.**Note:**There*cos*and*sin*are periodic functions with the smallest period 2p and an integral multiple of 2p also in turn period of*cos*and*sin*is, the result of raising a complex number to the power of an integer exponent is uniquely determined. However, this cannot be transferred to rational, real or complex exponents. For this see the square root of complex numbers and the complex power function. Now that it is clear what the power of a complex number means and how it can be calculated, one can go a step further and use the complex power function f (*z*) = e^{z}introduce. e^{z}= e^{(Re(z) + i Im (z))}= e^{(Re(z)}· E^{i Im (z)}Otherwise the laws of power calculus apply, which are transferred.

**Example 2:**e

^{(2 + i p / 2)}= e^{2}· E^{i p / 2}= e^{2}· I- How do I develop good architectural concepts
- What is special about Hollywood films
- Is it possible to be too introspective?
- Can I sell the eBay account I have set up?
- Who will lead Cuba to Raul Castro
- My HTML CSS code link is not linked
- What is greed 1
- Is colorism the root of white privilege
- How many years was South Africa colonized?
- Why did most of the utopias begin?
- Is going to school really that important?
- Where is Ahmednagar
- What is the NYT Magazines 1619 project
- Why do we get junk mail
- When will the NEET 2018 exam be?
- Like living after a digital marketing course
- Is terrorism an inevitable evil of democracy
- Should children hear Marilyn Manson
- Which is the best Amitabh Bachchan song
- How do I forget someone forever
- At what temperature can oxygen be liquefied
- Which song would you prefer
- What is a non-participant observation
- How is the medical technology profession developing?