Absolute value of a complex number

[jesuslovesu]

Homework Statement

Find the real/imaginary parts of sinh(x+yi) and its abs value.

Homework Equations

The Attempt at a Solution

I am able to decompose sinh(x+yi) = cosy*sinh(x) + isin(y)cosh(x) - (which is correct according to my book)

Now finding the absolute value is kind of causing some problems.
If I'm not mistaken |z| = sqrt(x^2+y^2) = sqrt(z * conj(z) )

So I'm treating cosy*sinh(x) + isin(y)cosh(x) as a complex number.

So I multiply ( cosy*sinh(x) + isin(y)cosh(x) ) * ( cosy*sinh(x) - isin(y)cosh(x) ) and I get sqrt( cosy^2*sinhx^2 + siny^2*coshx^2 ) so I would think sqrt( sinhx^2 + coshx^2 ) is the answer. However, it's supposed to be sqrt( sinhx^2 + siny^2)

Does anyone know what I did wrong?

 

[Dick]

"sqrt( cosy^2*sinhx^2 + siny^2*coshx^2 )" is right. Your next step isn't. It looks like they express the answer in terms of just sin and sinh. So take the above and replace cos^2(y) by 1-sin^2(y) and cosh^2(x) by 1+sinh^2(x).