- #1
unique_pavadrin
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- 0
Homework Statement
Find the locus of the point z satisfying:
[tex]\left| {\frac{{z - 1 - 2{\bf{i}}}}{{z + 1 + 4{\bf{i}}}}} \right| = 1[/tex]
2. The attempt at a solution
[tex]\begin{array}{l}
\left| {\frac{{z - 1 - 2{\bf{i}}}}{{z + 1 + 4{\bf{i}}}}} \right| = 1 \\
\left| {\frac{{\left( {x - 1} \right) + \left( {y - 2} \right){\bf{i}}}}{{\left( {x + 1} \right) + \left( {y + 4} \right){\bf{i}}}} \times \frac{{\left( {x + 1} \right) - \left( {y + 4} \right){\bf{i}}}}{{\left( {x + 1} \right) - \left( {y - 4} \right){\bf{i}}}}} \right| = 1 \\
\left| {\frac{{x^2 + y^2 - 9 + \left( {2y + 2 - 6x} \right){\bf{i}}}}{{\left( {x + 1} \right)^2 + \left( {y + 4} \right)^2 }}} \right| = 1 \\
\end{array}[/tex]
im not sure if that is correct but it seemed logical to me at the time, what do i do with the imaginary part of equation?
many thanks,
unique_pavdrin