Simple Algebraic Method for Finding Square Roots of Complex Numbers
It is quite easy to find the solutions
of the equation
or
(1) where
and
are known by assuming a solution of the form
– the advantage of this is that x and y must both be real. We form simultaneous equation in
and
by equating the real and complex parts of the equation (1). In general the equation (1) will have two solutions.
Example:
Solve the equation
If we assume a solution of the formthen
We form the simultaneous equations
(2)
(3)
Rearrange (3) to makethe subject obtaining
and substitute into (2)
must be positive hence
Example:
Solve the equation
If we assume a solution of the formthen
We form the simultaneous equations
(2)
(3)
Rearrange (3) to makethe subject obtaining
and substitute into (2)
must be positive hence
