Power of Complex numbers
How to calculate power of complex numbers? This is a very simple problem, if you know the main idea of this kind of tasks. First of all, it is nesesary to convert any complext number into exponetial form and then apply power to it. Then it is important to understand, that the results mean. So, let's consider simple example:
Example: \( (1+i)^5 = ? \)
This equation can be solved via converting to exponential form:
\[(1+i)^5 = \left(2^\frac{1}{2}e^{i\frac{\pi}{4}}\right)^5 = 2^\frac{5}{2}e^{i\frac{5\pi}{4}} = \frac{25}{2}e^{i(\frac{\pi}{4}+\pi)} = -4-4i\]
For graphical explanation please check this video:
Published: 2023-05-08 13:29:28
Updated: 2023-05-08 14:58:34
Last 10 artitles
- 2023-12-25 01:48:38 - In-place and out-place Numpy functions
- 2023-12-25 00:58:08 - First order ordinary differential equations
- 2023-12-25 00:22:15 - How to increase swap space in Ubuntu
- 2023-12-24 04:03:12 - How to accelerate math calculations with Numba and Cython
- 2023-12-19 00:38:20 - 3 ways of function caching in Python
- 2023-12-19 00:16:55 - Accelerating Python
- 2023-12-16 12:26:55 - BioPython
- 2023-12-02 11:05:34 - Reading FITS files with astropy
- 2023-12-02 05:23:42 - Astropy
- 2023-12-01 00:33:16 - Circle length calculation with the Monte-Carlo method
9 popular artitles
- Python Panda (3601)
- Python NumPy (3115)
- Python DICTionary HowTo (1653)
- Python LIST HowTo (1538)
- Python (1461)
- Python Generators (1339)
- Python: How to make absolute links in BeautifulSoup (1208)
- NumPy: What the difference between mgrid and meshgrid (1052)
- Programming language (1003)
