Search found 4 matches

by Captainjp
Thu Jul 14, 2016 7:01 pm
Forum: Complex Analysis
Topic: Non existence of complex functions
Replies: 3
Views: 4593

Re: Non existence of complex functions

Show that the only entire function \( \displaystyle f \) that satisfies \( \displaystyle \Big| f(z)-i \Big| < \Big| f(z) \Big|e^{\Re(z)} \, , \, \forall z \in \mathbb{C} \) is the constant function \( \displaystyle f(z)=i \, , \, z \in \mathbb{C} \). Since \( f(z)=0 \) is impossible for any \( z\in...
by Captainjp
Sun Feb 14, 2016 8:10 pm
Forum: Linear Algebra
Topic: Rank of a matrix
Replies: 1
Views: 2358

Re: Rank of a matrix

Adding and subtracting columns from other columns is obviously a procedure that does not affect the rank of the matrix. By first subtracting the \( n-1 \) -th column from the \( n \) -th, then the \( n-2 \) -th from the \( n-1 \) -th, and so on, and repeating the same procedure again, we get that \(...
by Captainjp
Sun Feb 14, 2016 8:04 pm
Forum: Real Analysis
Topic: Existence of sequence
Replies: 3
Views: 3057

Re: Existence of sequence

Yes, this is what I meant.

Although I have to say I like your solution a lot more! :D
by Captainjp
Sun Feb 14, 2016 8:01 pm
Forum: Real Analysis
Topic: Existence of sequence
Replies: 3
Views: 3057

Re: Existence of sequence

I think that this leads to a solution: We substitute \(\frac{1}{z_n}=\theta_n\), and then it is enough to find a sequence \(\theta_n\) such that \(|\theta_{n+1}|>|\theta_n|+1\), such that \(e^{\theta_n}=3+7i\) for every \(n\). Since we are talking about complex numbers and by the periodicity of \(\s...