Use the "^" character (shift-6) to represent exponentiation (e.g., "z^3", not just "z3"). I assume the roots to be found are for the equations
Finding roots of complex numbers is made easy with deMoivre's Theorem.
If a complex number is represented in the form
where r is a magnitude and theta is an angle of the complex number in the complex plane, then deMoivre's Theorem says that the n n-th roots of the complex number are found as follows:
(1) the magnitude of each root is the n-th root of the magnitude of the given complex number; and
(2) the "primary" n-th root has an angle that is (1/n) times the angle of the given complex number; and the other n-th roots are distributed around the circle at increments of 360/n degrees.
Here is an example....
Find the roots of
The given complex number in the required form is .
The magnitude of the given complex number is 1, so the magnitude of each of the 4-th roots is 1^(1/4)=1.
The angle of the given complex number in the complex plane is 90 degrees, so the "primary" 4-th root of i is at an angle of 90/4 = 22.5 degrees. The other 4-th roots of i are then distributed around the plane at increments of 360/4 = 90 degrees.
So the solutions to the equation are
(1)
(2)
(3)
(4)
Use the theorem to find the solutions to your examples.
To get you started -- in case you need help with this part -- the complex numbers in your examples are
(1) magnitude sqrt(2), angle 45 degrees
(2) magnitude 1, angle 90 degrees
(3) magnitude 1, angle 180 degrees
