For the mapping f(z) = sinh(z), find and sketch the image of im(z) = d z = x + iy w = u + iv This is the solution given: << got this one But confused about the rest..Please help. Thanks!
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Originally Posted by xaz For the mapping f(z) = sinh(z), find and sketch the image of im(z) = d z = x + iy w = u + iv This is the solution given: << got this one But confused about the rest..Please help. Thanks! $w=\sinh(z)=\sinh(x+\imath y)=\sinh(x)\cos(y) + \imath \cosh(x)\sin(y)$ $u=\sinh(x)\cos(y)$ $v=\cosh(x)\sin(y)$ The image of $\Im(z)=d$ is just that of $y=d$ or $u=\sinh(x)\cos(d)$ $v=\cosh(x)\sin(d)$ you can play with sketching the image of the line $y=d$
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