Solving Complex Number Equations: Tips for Beginners | Mathboy20

[mathboy20]

Hi I'm fairly new to complex numbers and was yesterday presented with the following assignment.

Find w,z \in \mathbb{C}

w + (1+i)z = -1

(1-i) - z = 1

Any hints on how to solve these equations?

Sincerely Yours

Mathboy20

 

[benorin]

Systems of linear equations with complex numbers can be solved with the same methods used for real systems, perhaps easiest are matrix methods or Cramer's rule.

 

[benorin]

For example--oh, it is easier to do this:


(1) w + (1+i)z = -1
(2) (1-i) - z = 1

(2) gives z=-i (by adding z-1 to both sides), substitute this into (1) to get

w + (1+i)(-i) = -1
w + -i+1 = -1
w = -2+i

so the final answer is z=-i and w=-2+i

 

[Hurkyl]

You generally solve complex equations the same way you would solve real equations.