What is the general solution for sin^2(z)=-1 ?

The general solution for sin^2(z)=-1 is No Solution for z\in\mathbb{R}

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sin^2(z)=-1

sin^{2} (z) = - 1

No Solution for z \in R

Solution steps

sin^{2} (z) = - 1

Solve by substitution

sin^{2} (z) = - 1

Let:

sin (z) = u

u^{2} = - 1

u^{2} = - 1 : u = i, u = - i

u^{2} = - 1

For

x^{2} = f (a)

the solutions are

x = f (a), - f (a)

u = - 1, u = - - 1

Simplify

- 1 : i

- 1

Apply imaginary number rule:

- 1 = i

= i

Simplify

- - 1 : - i

- - 1

Apply imaginary number rule:

- 1 = i

= - i

u = i, u = - i

Substitute back

u = sin (z)

sin (z) = i, sin (z) = - i

sin (z) = i, sin (z) = - i

sin (z) = i :

No Solution

sin (z) = i

No Solution

sin (z) = - i :

No Solution

sin (z) = - i

No Solution

Combine all the solutions

No Solution for z \in R

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What is the general solution for sin^2(z)=-1 ?
The general solution for sin^2(z)=-1 is No Solution for z\in\mathbb{R}