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How do I write arcsin4 in the form a+ib. I know the answer but do not Know how to get to it

Take sinus of both sides:

4 = sin(a)cosh(b) + i cos(a)sinh(b)

Equate real and imaginary parts. You then see that you can put a = pi/2. And it then follows that b = arccosh(4)

Thanks for getting back so promptly , unfortunately i do not what you mean by take sinus of both sides. I have got the stage you have it is the very final stage I van not do

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