A Level Maths Notes: FP1 – 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
