# Complex number question

1. Feb 8, 2006

### 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

2. Feb 8, 2006

### 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.

3. Feb 8, 2006

### 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

4. Feb 8, 2006

### Hurkyl

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