Question 1208326
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if z = [ r , theta ] , (z ^2 + (| z |)^2)/(z + | z |) = cos (theta)(1 + i tan (2/(theta))) , prove that r = 1
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In your post, the part    tan(2/(theta))    ( which is    {{{tan(2/theta)}}})    is absurdist.


There are no doubts that it is incorrect, while a correct version is    tan(2*theta).


With this corrected/modified writing, see the solution produced by AI under this link  &nbsp;&nbsp;<A HREF=https://www.google.com/search?q=if+z+%3D+%5B+r+%2C+theta+%5D+%2C+(z+%5E2+%2B+(%7C+z+%7C)%5E2)%2F(z+%2B+%7C+z+%7C)+%3D+cos+(theta)(1+%2B+i+tan+(2%2F(theta)))+%2C+prove+that+r+%3D+1&rlz=1C1CHBF_enUS1071US1071&oq=if+z+%3D+%5B+r+%2C+theta+%5D+%2C+(z+%5E2+%2B+(%7C+z+%7C)%5E2)%2F(z+%2B+%7C+z+%7C)+%3D+cos+(theta)(1+%2B+i+tan+(2%2F(theta)))+%2C+prove+that+r+%3D+1&gs_lcrp=EgZjaHJvbWUyBggAEEUYOdIBCTIwMjdqMGoxNagCCLACAQ&sourceid=chrome&ie=UTF-8>solution</A> .



&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Learn to write Math correctly.



Writing Math correctly means check, re-check, then double check and cross-check.


If you submit your post without checking, &nbsp;it is &nbsp;99% &nbsp;erroneous.