find taylor series for cosh(z) about z = 1+i?

Answer 1

You need the derivatives of all orders evaluated at 1 + i. Find
Sum (1 to inf) {cosh(1+i)*(1+i)^(2n)}/(2n)! +
Sum (1 to inf) {sinh(1+i)*(1+i)^(2n+1)}/(2n+1)!