[DSE 2019] 你地溫 數學 又溫成點呢？ [3]

1001 回覆
24 Like 21 Dislike
2019-01-03 03:54:09
又係你
2019-01-03 04:05:25
用Binomial Theorem做得唔得？
2019-01-03 04:16:35
Another intuitive question:

Let f(x) = a^x where a >2
Then we have f(i) = a^i.
Is it correct?
Answer

i = i^(4n+1)
a^i = a^i^(4n+1) = a^(4n+1)^i
for any real integer n>0

Then a^i is multi-valued, which defies the definition of function
So f(i) is not defined.
有錯請指正

錯，仲有a^i = e^(i ln a)
2019-01-03 04:25:16
a^i = e^(i*ln a) = e^(i*(ln a + 2n*pi))
this a^i is multi-valued
仲有龜蛇你對complex number 咁有興趣
你正正經經搵本complex variables and application 讀下啦
2019-01-03 04:36:56
complex variables 已經係ug數，你點砌都砌唔入core level啦
除非數學科聽日改革啦
btw change of base 咪一早有囉
2019-01-03 04:45:00
巴打覺得大陸高考數難過dse數學幾多?
2019-01-03 04:47:28
高考文科數學卷都要Fourier Transform?

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