Complex analysis question (only need a hint)

In summary, Complex analysis is a branch of mathematics that studies functions of complex numbers. It is different from real analysis in that it deals with functions of complex variables and has its own theorems and techniques. The Cauchy-Riemann equation is a set of differential equations that describe the conditions for a complex function to be differentiable. Some applications of complex analysis include fluid dynamics, electromagnetism, and signal processing.
  • #1
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i know it's supposed to be a simple question. frustrating because it is not coming to me. just want a hint.

question is:
how do you write
1 + cos(theta) + cos (2*theta) + cos(3*theta)... cos(n*theta) using the fact that (z^(n+1) -1) / (z^(n) -1) = 1 + z + z^(2) +... + z^(n)

thanks in advance
 
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  • #2
How about
[tex] Re \sum_{k=0}^{n} e^{ikz} [/tex]

or sum over real of the same "animal"...Which one u prefer...??

Daniel.

PS.Or theta,but it's cusomary to denote complex variables with "z"...
 
  • #3


Hint: Try using the fact that cos(theta) = (e^(i*theta) + e^(-i*theta)) / 2 and simplify the expression using the given formula.
 

FAQ: Complex analysis question (only need a hint)

What is complex analysis?

Complex analysis is a branch of mathematics that deals with the study of functions of complex numbers. It involves the analysis of functions, series, and integrals of complex variables.

What is a complex number?

A complex number is a number that can be expressed in the form of a + bi, where a and b are real numbers and i is the imaginary unit (√-1).

How is complex analysis different from real analysis?

Complex analysis deals with functions of complex variables, while real analysis deals with functions of real variables. Complex analysis also has its own set of theorems and techniques that are specific to complex numbers.

What is the Cauchy-Riemann equation?

The Cauchy-Riemann equation is a set of differential equations that describe the conditions for a complex function to be differentiable. It states that a function is differentiable at a point if and only if it satisfies these equations.

What are some applications of complex analysis?

Complex analysis has various applications in physics, engineering, and other fields. It is used in the study of fluid dynamics, electromagnetism, signal processing, and many other areas where complex numbers are involved.

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