Complex numbers with an unknown, fraction equation not getting it right

[Femme_physics]

Attempt solution attached
Manual says the answers is -1 + i

 

[eumyang]

The solution you posted,
$$z = \frac{2}{1 + i}$$
is not simplified. You know that you can multiply top and bottom by the conjugate, right? Even so, you still won't get the right answer.

EDIT: I think I found it. From the 2nd to 3rd line, on the RHS you have
$$(2iz + 1)(1 - i) = 2iz - 2iz + 1 -i$$
, which is wrong. It should be
$$(2iz + 1)(1 - i) = 2iz - 2i^2 z + 1 - i$$
.

 

[Femme_physics]

Thanks for the great catch! :) I wasn't sure I even know how to solve these. Glad to see I didn't do anything horribly wrong. Apparently it's all about treating i and z like x and y, and if i ever gets to the power of 2, just turn into -1. Easy peasy :)

Appreciate you taking the time to spot my carelessness!