Question

Question #a5393

Answer 1

No there are misplaced parentheses.

Explanation:

e^(z^2) means `e^(z^2)`.

So for example when `z = 3`, `e^(z^2) = e^9`.

What is true is that e^z-e^-z=0 is equivalent to (e^z)^2 - 1 = 0

and (e^z)^2 = e^(2z), so both of these are equivalent to e^(2z)-1=0

`e^z-e^-z=0` multiply both sides by `e^z` to get

`e^z(e^z-e^-z) = e^ze^z-e^ze^-z = e^(z+z)-e^(z-z) = e^(2z)-e^0 = e^(2z)-1`