Question

If `z=re^i theta` then `|e^(iz)|` is equal to:

Answer 1

`z=re^(itheta),iz=ire^(itheta)`
`=l8r{costheta+isintheta}`
`=r(sintheta+icostheta)`
`e^(iz)=e^r*(icostheta-sintheta)`
`=e^(-rsintheta)*e^(ircostheta)`
`|e^(iz) | =|e^(-rsintheta*e*^(ircostheta)`
`=e^(-rsontheta)*|costheta|isintheta|^(rcostheta)`
`=e^(-rsintheta)*(1)^rcostheta`
`=e^(-rsintheta)`.