Advertisement Remove all ads

Considering Only Principal Values Separate into Real and Imaginary Parts I ( Log ) ( I + 1 ) - Applied Mathematics 1

Advertisement Remove all ads
Advertisement Remove all ads
Sum

Considering only principal values separate into real and imaginary parts

`i^((log)(i+1))`

Advertisement Remove all ads

Solution

Let  `Z=i^(log(i+1))` 

`therefore logZ = log(1+i).logi`

But `log(i+1)=logsqrt2+itan^(-1)1 = logsqrt2+ipi/4`

and `logi=ipi/2`

`therefore log Z=(logsqrt2+ipi/4).ipi/2`
`=[1/2log2+ipi/4pi]/2` 

`(-pi^2)/8+ipi/4log2=e^(pi^2/8+itheta)= e^(pi^2/8itheta)`

where `theta=pi/4log2`

`=e^(pi^2/8)[costheta+isintheta]`

∴ Real part of Z `=e^(pi^2/8)costheta=e^(pi^2/8)cos[pi/4log2]`

∴ Imaginary part of Z `=e^(pi^2/8)sin[pi/4log2]`

Concept: Separation of Real and Imaginary Parts of Logarithmic Functions
  Is there an error in this question or solution?
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×