Let f be the function defined in the complex plane by f(x)=(z²-2)e^(-x)e^(-iy), where z = x + iy.?

👨🏻‍🏫 學術台數學

[匿名]

2019-02-21 10:55 pm

更新1:

Then f is an entire function. Pls explain you answer. Anybody can help. I am lost in this question.

更新2:

True or False?

回答 (3)

用戶58503

2019-02-21 11:12 pm

Its an easy feat to find the definition of 'entire function'. So, can you state it here? Do that, then we will take it from there.

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[匿名]

2019-02-22 2:25 am

f(x)
= (z²–2)e^(-x)e^(-iy), where z = x + iy
= (z²–2)e^(-x–iy)
= (z²–2)e^-z

We know that all polynomials of z and e^z are entire functions — as are sums, products and compositions of entire functions. So yes, f is an entire function.

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Ian H

2019-02-22 12:16 am

https://en.wikipedia.org/wiki/Entire_function

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