- #1

agnimusayoti

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- Homework Statement
- Find absolute value of ##\sin (x-iy)##.

- Relevant Equations
- $$\sin z=\frac {e^{iz}-e^{-iz}}{2i}$$

If ##z=x+iy## then, absolute value of this complex number is ##|z|=\sqrt {x^2+y^2}##

So far I've got the real part and imaginary part of this complex number. Assume: ##z=\sin (x+iy)##, then

1. Real part: ##\sin x \cosh y##

2. Imaginary part: ##\cos x \sinh y##

If I use the absolute value formula, I got ##|z|=\sqrt{\sin^2 {x}.\cosh^2 {y}+\cos^2 {x}.\sinh^2 {y} }##

How to simplify that answer to ##|z|=\sqrt{\sin^2 {x}+\sinh^2 {y}}##?

Thanks

1. Real part: ##\sin x \cosh y##

2. Imaginary part: ##\cos x \sinh y##

If I use the absolute value formula, I got ##|z|=\sqrt{\sin^2 {x}.\cosh^2 {y}+\cos^2 {x}.\sinh^2 {y} }##

How to simplify that answer to ##|z|=\sqrt{\sin^2 {x}+\sinh^2 {y}}##?

Thanks

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