lab week 5

Question 1

construct a complex number in Python

Answer 1

num = complex(a, b) or num = a + bj

Question 2

how to get the angle of the complex number in degrees, not radians?

Answer 2

np.degrees(np.angle(complex_num))

Question 3

create the conjugate of pointB

Answer 3

np.conj(pointB)

Question 4

extract the real component from the complex number in Python

Answer 4

np.real( num )

Question 5

Euler’s formula

Answer 5

Question 6

magnitude vs Euler’s formula

Answer 6

Question 7

Fourier coefficient in general

Answer 7

the output of the Fourier transform

Question 8

Fourier coefficient vs Euler’s formula

Answer 8

abs(complex) = magnitude

angle(complex) = phase

Fourier components are complex numbers

Question 9

all cosines are in-phase - how would this look like? what does it mean?

Answer 9

they all start at 1. At some time point, they are all 1 again. This occurs at 1s.