IB MATHEMATICS Topic ; Complex Numbers – Solving Complex Simultaneous Equations

Complex simultaneous equations are in fact just normal simultaneous equations and can be solved in the usual way, by equating coefficients of one variable and eliminating, or by substitution.
To solve the complex simultaneous equations
(1)
(2)
Rearrange (1) to give(3) and substitute this into (2) to give

Partially expanding brackets gives


Factorising with w and taking the first term on the left over to the right hand side gives

Hence
Substituting this into (3) gives