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geniusboy [140]
3 years ago
11

PLEASE PLEASE HELP IF YOU KNOW!! THANK YOU

Mathematics
1 answer:
Vladimir [108]3 years ago
5 0
I'm guessing this is what the question is asking?

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Use the theorem in Sec. 28 to show that if f (z) is analytic and not constant throughout a domain D, then it cannot be constant
alexandr1967 [171]

Answer:

The value of f(z) is not constant in any neighbourhood of D. The proof is as explained in the explaination.

Step-by-step explanation:

Given

For any given function f(z), it is analytic and not constant throughout a domain D

To Prove

The function f(z) is non-constant constant in the neighbourhood lying in D.

Proof

1-Assume that the value of f(z)  is analytic and has a constant throughout some neighbourhood in D which is ω₀

2-Now consider another function F₁(z) where

F₁(z)=f(z)-ω₀

3-As f(z) is analytic throughout D and F₁(z) is a difference of an analytic function and a constant so it is also an analytic function.

4-Assume that the value of F₁(z) is 0 throughout the domain D thus F₁(z)≡0 in domain D.

5-Replacing value of F₁(z) in the above gives:

F₁(z)≡0 in domain D

f(z)-ω₀≡0 in domain D

f(z)≡0+ω₀ in domain D

f(z)≡ω₀ in domain D

So this indicates that the value of f(z) for all values in domain D is a constant  ω₀.

This contradicts with the initial given statement, where the value of f(z) is not constant thus the assumption is wrong and the value of f(z) is not constant in any neighbourhood of D.

6 0
2 years ago
Lauren spent 3/5 of her money on a refrigerator. The refrigerator cost $756. How much money did she have left?
Lelechka [254]
Fractions are the part/whole.  We can set this up to be...

3/5 = 756
756 x5/3 = 1260.

if she had 1260 to begin with and spent 756, she would have 504.00 left.
3 0
3 years ago
The blue dot is what value on the number line
Anastaziya [24]
8 and 12 are separated by 1 line, and they have a difference of 4 units, so..

count every two lines and add 4 units

this means that the blue dot is 20
5 0
3 years ago
Read 2 more answers
(THIS IS A ANSWER FOR SOME PEOPLE FOR THIS MATH QUESTION)
Phantasy [73]

Answer:

omg thank you I needed this answer

7 0
3 years ago
Which of the following are reasons used in the proof that the angle-bisector construction can be used to bisect any angle? Check
Bad White [126]

The answer for apex users are:

All of the radii of a circle are congruent

CPCTC

SSS triangle congruence postulate

3 0
3 years ago
Read 2 more answers
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