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sinz=-2 equation

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Numerical solution:

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The solution

You have entered [src] 
sin(z) = -2
$$\sin{\left(z \right)} = -2$$
Simplify
Detail solution
Given the equation
$$\sin{\left(z \right)} = -2$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
True

but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
pi + I*im(asin(2)) + re(asin(2)) + -re(asin(2)) - I*im(asin(2))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)$$ 
=
pi
$$\pi$$ 
product
(pi + I*im(asin(2)) + re(asin(2)))*(-re(asin(2)) - I*im(asin(2)))
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)$$ 
=
-(I*im(asin(2)) + re(asin(2)))*(pi + I*im(asin(2)) + re(asin(2)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)$$ 
-(i*im(asin(2)) + re(asin(2)))*(pi + i*im(asin(2)) + re(asin(2)))
Rapid solution [src] 
z1 = pi + I*im(asin(2)) + re(asin(2))
$$z_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}$$ 
z2 = -re(asin(2)) - I*im(asin(2))
$$z_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}$$ 
z2 = -re(asin(2)) - i*im(asin(2))
Numerical answer [src] 
z1 = 4.71238898038469 - 1.31695789692482*i
z2 = -1.5707963267949 + 1.31695789692482*i
z2 = -1.5707963267949 + 1.31695789692482*i
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