# Solving for the Real and Imaginary Number

• Tan Thom
In summary, the question is asking to find the 4th coefficient in a sample of 4 discrete time Fourier Series coefficients in a real time valued periodic sequence. The solution involves solving for a_3 using the given steps and ensuring that the resulting function is real-valued. However, it is unclear if the question is fully formed and there may be additional information needed to solve it accurately.
Tan Thom

## Homework Statement

Find the 4th Coefficient in a sample of 4 discrete time Fourier Series coefficients in a real time valued periodic sequence. k = 0,1,2,3

a_k = {3, 1-2j, -1, ?}

[/B]

## The Attempt at a Solution

Step 1: (1-2j)e^(j*.5pi*n) +a_3 e ^ -(j*.5pi*n) + 3 + (-1)^(n+1)

Step 2: [(1-2j)(cos (pi/2)n + j sin (pi/2)n) + a_3 (cos (pi/2)n)-j sin (pi/2)n]

Solving for a_3 in the final step is where I am confused.

#### Attachments

9.6 KB · Views: 675
I had a lot of experience with such things and the question doesn't seem to be fully formed to me. Perhaps there is some extra info somewhere? Perhaps the solution revolves around making sure that the resulting function will be real valued as stated in question. That sets constraints between coefficients.
However only summing over positive k values Will make it imposible to get a purely real signal. Normally that would happen when a(-k) is the complex conjugate of a(k). Or should it be using a discrete Fourier sin series, summing over real basis functions rather tan over exp(ikx) complex functions? Though you wouldn't need complex coeffs in that case. Need to see the full question I think.

berkeman

## 1. What are real and imaginary numbers?

Real numbers are numbers that can be found on the number line and include all rational and irrational numbers. Imaginary numbers are numbers that involve the imaginary unit, i, which is the square root of -1.

## 2. How do you solve for the real and imaginary parts of a complex number?

To solve for the real and imaginary parts of a complex number, you can use the formula a + bi, where a is the real part and bi is the imaginary part. For example, in the complex number 3 + 4i, 3 is the real part and 4i is the imaginary part.

## 3. How do you add and subtract complex numbers?

To add or subtract complex numbers, you simply combine the real parts and the imaginary parts separately. For example, (3 + 4i) + (2 + 5i) = (3+2) + (4i+5i) = 5 + 9i.

## 4. Can you multiply and divide complex numbers?

Yes, you can multiply and divide complex numbers using the FOIL method for multiplication and by rationalizing the denominator for division. For example, (3 + 4i) * (2 + 5i) = (3*2) + (3*5i) + (4i*2) + (4i*5i) = 6 + 15i + 8i + 20i^2 = 6 + 23i - 20 = -14 + 23i.

## 5. How are real and imaginary numbers used in science?

Real and imaginary numbers are used in science to represent physical quantities and phenomena that involve both real and imaginary components. For example, in electrical engineering, imaginary numbers are used to represent the complex impedance of a circuit. In quantum mechanics, imaginary numbers are used to represent the wave function of a particle. They are also used in many other fields such as fluid dynamics, signal processing, and optics.

• Engineering and Comp Sci Homework Help
Replies
3
Views
404
• General Math
Replies
2
Views
3K
• Engineering and Comp Sci Homework Help
Replies
3
Views
2K
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
1K
• Engineering and Comp Sci Homework Help
Replies
3
Views
8K
• Engineering and Comp Sci Homework Help
Replies
8
Views
2K
• Engineering and Comp Sci Homework Help
Replies
32
Views
3K
• Calculus and Beyond Homework Help
Replies
1
Views
422
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K