Question

How to solve the value of theta in following equation: x = e^(j * theta)

Answer 1

ohh so u have e take ln for both sides

are u sure its j not i the imaginary ?

Answer 2

Thanks for the quick response. The 'j' is imaginary 'i' only.

Answer 3

and X is a complex number.

Answer 4

\[e ^{j \theta}= \cos \theta+ j sin \theta \]

Answer 5

ok so
x= r cos theta
how ever r is the lengh sine z= x
then |z| =|x|

Answer 6

so
cos theta = x / |x|
then take theta = cos^-1 (x/|x| )

Answer 7

hehe u know how to take cos ^-1 right ?

Answer 8

hey...thanks a ton for that.
Yes i know how to get inverse of cos.
If i have got it right, then i shall just solve -> cos^-1(x/sqrt(x^2 + y^2)) where x is my complex number

Answer 9

neer! how to sove this ejθ=cosθ+jsinθ

Answer 10

most people find the angle of a complex number using
arc tan (imag/real)

Answer 11

i did the same thing using numpy..but just wanted to confirm. Thanks a lot!

Answer 12

remember
z= x +i 0
so y=0
also wat neer said is correct but he forget the r part how ever
ejθ=rcosθ+rjsinθ = x+ iy
but u have y=0
so x=rcosθ

Answer 13

This is what i have done:
theta = (np.arctan(x[0].imag/x[0].real)) * 180/np.pi

Answer 14

you have to be careful of the sign (which quadrant you are in)

Sometimes there is a function atan2(y,x) that takes the individual components, so it's able to compute the correct quadrant

Answer 15

see https://en.wikipedia.org/wiki/Atan2