.
The equation is
- + 1 = 0.
Multiply by z both sides. You will get
= 0, or, equivalently,
= 0.
Now introduce new variable u = . The last equation will take the form
= 0.
Apply the quadratic formula
= = = .
Now consider separately both cases
a) u = = . Hence, squaring, you get
z = = = = ,
and
b) u = = . Hence, squaring, you get
z = = = = .
Answer. There are two solutions. They are complex numbers
and .
Solved.
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Surely, it can be done in many ways and on different paths.
I showed here one of the simplest paths/ways.
Other people may prefer other ways.