Let z [ ] C with Im(z) = 10 and it satisfies [2z - n 2z + n] = 2i - 1 for some natural num…

Question

Let z $$ \in $$ C with Im(z) = 10 and it satisfies $${{2z - n} \over {2z + n}}$$ = 2i - 1 for some natural number n. Then :

Accepted Answer

Let Re (z) = x, then

$${{2(x + 10i) - n} \over {2(x + 10i) + n}} = 2i - 1$$

$$ \Rightarrow \left( {2x - n} \right) + 20i =  - \left( {2x + n} \right) - 40 - 20i + 2ni$$

$$ \Rightarrow 2x - n = 2x - n - 40$$

\& 20 = -20 + 2n $$ \Rightarrow $$ x = -10 \&  n = 20

Solutions · 1