Hello!

I was presented with the following solution that I don't understand:

Let z+i=rcis(theta)

then (rcis(theta))^4=1+i=sqrt(2)cis(pi/4)

r^4cis(4theta)=sqrt(2)cis(pi/4)

so r=eigthroot(2)

And the square formed by the 4 roots that work have area 2^(5/4) since area of square =2r^2 where 2r is the diagonal.

But the r is for z+i, not for z, so how do you know that the graphs of z have the same area as that of (z+i)?

                                                           (graph of z+i with magnitude r)    

Thank you,

Tina Jin