SOLUTION: Use De Moivre’s Theorem to solve for z and leave answer in polar form with the angle in radians Z^4=-1+ j square root of 3

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Use De Moivre’s Theorem to solve for z and leave answer in polar form with the angle in radians Z^4=-1+ j square root of 3      Log On


   

Question 1180663: Use De Moivre’s Theorem to solve for z and leave answer in polar form with the angle in radians

Z^4=-1+ j square root of 3
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


-1%2Bi%2Asqrt%283%29 = 2cis%282pi%2F3%29

z%5E4+=+2cis%282pi%2F3%29

To find the "first" solution using deMoivre's Theorem...



Then the other roots are spaced around the complex plane at increments of (2pi)/4=pi/2:

z=2%5E%281%2F4%29cis%28pi%2F6%29
z=2%5E%281%2F4%29cis%282pi%2F3%29
z=2%5E%281%2F4%29cis%287pi%2F6%29
z=2%5E%281%2F4%29cis%285pi%2F3%29