Understanding imaginary exponents - Mathematics Stack Exchange
Imaginary exponents are just the same. i, 2i, 3i are just like 1, 2 ,3: identity, square, and cube. They just need to run into another imaginary exponent to manifest their value, or you are carrying a lot of extra stuff you don't see. The reason we like e is because it's derivative is the same as it's function's output.
How can I intuitively understand complex exponents?
2017年11月3日 · $\begingroup$ If you want to calculate the exponential of a complex number, you can do either of the following: (1) use DeMoivre's identity, which passes the buck to the trig functions, or (2) use the power series for the exponential, which converges rapidly due to k! in the denominator of the terms.
How to calculate an imaginary number to high exponent?
2013年4月22日 · How can I calculate something like $(i+1)^{33}$ or similar high exponent without the use of a calculator?
What do we actually mean by raising some number to an …
When the exponent is not a natural number (nonnegative integer), exponentiation is not repeated multiplication, any more than multiplying by $\lambda$ is repeated addition when $\lambda$ is not a natural number.
Understanding $e$ and $e$ to the power of imaginary number
2015年9月13日 · There are many properties that make the exponential function special; one that I find particularly instructive is:
Negative imaginary exponents - Mathematics Stack Exchange
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Adding imaginary number "i" raised to high exponents
2018年6月29日 · How to calculate an imaginary number to high exponent? 0. Imaginary Number Adding One Explanation. 2.
How to calculate a real number raised to an imaginary number
2022年9月24日 · How to calculate integer exponent of complex number with integer parts to not get real values Hot Network Questions What's the justification for implicitly casting arrays to pointers (in the C language family)?
Simple way to solve the product of a imaginary number's exponent:
2018年9月7日 · I came up with is to take the imaginary number's exponent, divide it by 2, and if it's positive then the answer is 1. If the result is odd then the answer is -1. Example:
Will negative bases with irrational exponents get a real or …
From what I've learned, negative bases must have denominators of the exponent odd. Normally if we do $(-2)^{0.258}$ it would be the same as $(-2)^{50/129}$. That means that since $129$ is odd, it will give a real number.