determine arcsinh(2+i) in form of a+bi

Question

thanks

Answer 1

I'm sure you know that

arcsinh(z) = log(z+√(1+z^2))
so,
arcsinh(2+i) = log(2+i + √(4+2i))
= log(4.058 + 1.486i)

Now log(z) = log(x+yi)
= log(√(x^2+y^2) + i arctan(y/x)

So, plug in your z value above and crank it out.

Answer 2

google arcsinh to get the definition I gave

google complex logarithm to find how to evaluate it.

Surely you have enough keywords to do some research yourself. I didn't know that stuff either, but I know how to search for it.