Simple Algebraic Method for Finding Square Roots of Complex Numbers

It is quite easy to find the solutionsof the equationor(1) whereandare 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 inandby 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 obtainingand 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 obtainingand substitute into (2)

must be positive hence