Let f(t)=t+i where -pi<t<pi and has period 2pi. Why is it impossible to express the Fourier series of f(t) in real form?

OlmekinjP

OlmekinjP

Answered question

2021-09-05

Let f(t)=t+i where π<t<π and has period 2π. Why is it impossible to express the Fourier series of f(t) in real form?
A. Because f(t) is a complex function with Re(f(x))<0
B. Because f(t) is a complex function with Im(f(x))0
C. Because f(t) is a complex function with Im(f(x))=0
D. Because f(t) is a complex function with Re(f(x))>0

Answer & Explanation

Macsen Nixon

Macsen Nixon

Skilled2021-09-06Added 117 answers

Step 1
Given function is
f(t)=t+i,π<t<π
Step 2
We see that Im(f(t))=1s˙(Im(f(t))=coefficient of  i)
Im(f(t))0
Thus , f(t) is complex function with Im(f(t))0
Im(f(x))0
The Fourier series of f(t) cannot be expressed in real form.
option (B) is correct

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Multivariable calculus

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?