Question

Find the zeroes and their order for the following. (Use Taylor series or derivatives)

sin(z)

Answer 1

Summary:- Definitions of zeros-- A zero(z₀) is a value of z , where f(z₀₎=0.

If z₀ is a zero of order n then nth derivative of f(z) is non-zero at z₀ whenver all preceeding derivative upto n-1 are zero at z₀.

Now we solve question, we see that {n: n} are zeros of sin(z) of order 1.

Here we find out zeros by the help of derivatives.