Solving the system w + (1+i)z = -1 and (1-i) - z = 1

[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.