Question

If sin(a + iß) = x + iy then the value is equal to ​

Answer 1

Sin (A+B) = Sin(A)Cos(B) + Sin(B)Cos(A)

Sin(a+ib) = Sin(a)Cos(ib) + Sin(ib)Cos(a)

which can be write as

Sin(a+ib) = Sin(a)Cosh(b)+i(Cos(a)Sinh(b))

which is of the form x+iy

Sin(a+ib) = = x+ iy where

x = Sin(a)Cosh(b)

y = Cos(a)Sinh(b)