SOLUTION: if MOD (Z-3)=3 THEN PROVE (Z-6)/Z=itan(argZ)

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Question 476992: if MOD (Z-3)=3 THEN PROVE (Z-6)/Z=itan(argZ)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
There's a little problem with your statement:

Let z = a + bi.
Then z - 3 = (a- 3) + bi.
==> |z - 3| = |(a- 3) + bi| = sqrt%28%28a-3%29%5E2+%2B+b%5E2%29 = 3, by the given.
==> %28a-3%29%5E2+%2B+b%5E2+=+3%5E2
==> a%5E2+-+6a+%2B+9+%2B+b%5E2+=+9 ==> a%5E2+%2B+b%5E2+=+6a.
Now
=
=
Now arg%28z%29+=+tan%5E%28-1%29%28b%2Fa%29, which gives tan%28arg%28z%29%29+=+b%2Fa, or
b+=+a%2Atan%28arg%28z%29%29, hence
%28z-6%29%2Fz+=+a%2Ai%2Atan%28arg%28z%29%29+=+Re%28z%29%2Ai%2Atan%28arg%28z%29%29.
Check again the statement of your result.