The value of sin(iz) is equal to

The value of sin(iz) can be found using the formula for the sine of a complex number.

Step 1: Recall the definition of the sine function for complex numbers. The sine of a complex number z = x + iy is given by:

sin(z) = sin(x)cosh(y) + i*cos(x)sinh(y)

Step 2: Substitute iz for z in the above formula. This gives:

sin(iz) = sin(iy)cosh(x) + i*cos(iy)sinh(x)

Step 3: Recall that the sine of an imaginary number is imaginary and the cosine of an imaginary number is real. Therefore, we have:

sin(iy) = i*sinh(y) cos(iy) = cosh(y)

Step 4: Substitute these values back into the formula from step 2. This gives:

sin(iz) = isinh(y)cosh(x) + icosh(y)sinh(x)

Step 5: Simplify the above expression to get the final answer:

sin(iz) = isinh(x)cosh(y) + sinh(x)cosh(y) = isinh(x) + sinh(x)

So, sin(iz) = i*sinh(x) + sinh(x)