Sequences in complex (just a clarifying question)

In summary, the conversation discusses using a theorem to prove that if the sums of two sequences, zn and wn, are S and T respectively, then the sum of their combined sequence, zn + wn, is equal to the sum of S and T. The conversation also mentions breaking up the sums of the real and imaginary parts of zn and wn in order to reach this conclusion. However, the conversation notes that further steps are needed to fully prove this theorem.
  • #1
bennyska
112
0

Homework Statement


(excuse lack of latex)
show that if SUM(zn)= S and SUM(wn= T, then SUM(zn + wn) = S + T

Homework Equations


The Attempt at a Solution



so if I'm doing this right, this is pretty easy, i think. they want me to use a theorem that says if zn=xn +iyn, and SUM(zn)= S, where S = X + iY, this happens iff SUM(xn)= X and SUM(yn)= Y.

so my question is am i allowed to say SUM(zn + wn) = SUM(zn) + SUM(wn) = SUM(xn) + iSUM(yn) + SUM(un) + iSUM(vn)? I'm not sure if I'm violating anything by breaking it up like this. it all follows very quickly from here.

*edit: forgot to erase double standard questions after preview
 
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  • #2
You can break it up as:
SUM(xn+un)+iSUM(yn+vn)

just using the property that you posted (make sure you understand why). To go further you need to do something else
 

What are sequences in complex?

Sequences in complex refer to a series of numbers or terms that follow a specific pattern or rule. These sequences can be finite or infinite and can be represented in various ways, such as with equations, diagrams, or graphs.

What is the importance of studying sequences in complex?

Sequences in complex are important in various fields of science, including mathematics, physics, and computer science. They help us understand patterns and relationships, make predictions, and solve problems. They also have practical applications, such as in cryptography and data compression.

How are sequences in complex different from sequences in other mathematical concepts?

Sequences in complex differ from other mathematical sequences, such as arithmetic or geometric sequences, because they involve complex numbers. These are numbers that have both real and imaginary components, and they follow different rules and patterns compared to real numbers.

What are some common types of sequences in complex?

Some common types of sequences in complex include arithmetic sequences, geometric sequences, and Fibonacci sequences. Other types include polynomial sequences, exponential sequences, and recursive sequences.

How can sequences in complex be used in scientific research?

Sequences in complex can be used in scientific research to model and understand natural phenomena, such as the growth of populations or the behavior of particles. They can also be used in computational simulations and algorithms to solve complex problems and analyze data.

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