FFT question needs answering! Please show some work for points! Thanks! Using Eu

Question

FFT question needs answering! Please show some work for points! Thanks!

Using Euler's formula, e jtheta = COS(theta) j Sin(theta), express ejpi/4 as a complex number, a + jb, and find the numerical values of a and b. The arguments of trigonometric functions are in radians and not in degrees. e = cos(_) + j* sin(_) = evaluate ejpi/B raised to the power 4 using Euler's formula and express the result as a complex number in rectangular form. Show the various steps you took in finding the answer. (ab) raised to the power n equals abn. (ejpi/8 = e = e = cos(_) + j * sin(_) = + j = Using Euler's formula, show that ejpi is equal to -1. Having proved this, we can consider the nth root of ejpi as the nth root of -1. Thus, using Euler's formula, find the fourth root of -1. In other words, find ejpi raised to power (1/4). Use the knowledge you gained in b. The result will be a complex number. The conjugate of the complex number is also a correct answer. ejpi = cos(pi)+ j * sin(pi)= -1 + 0j = (ejpi)1/4 = e = cos(_) + j sin(_) =

Explanation / Answer

a) ejpi/4=cos(pi/4)+jsin(pi/4)=1/sqrt(2) *(1+j)

b) (ejpi/8)4=ejpi/2=cos(pi/2)+jsin(pi/2)=j

c) ejpi =cos(pi)+jsin(pi)= -1+j0=-1

now (ejpi)1/4=ejpi/4 =1/sqrt(2) *(1+j)

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