17 The Argand diagram below shows a circle \(C\)
\includegraphics[max width=\textwidth, alt={}, center]{99b03f18-6dd6-437d-8b01-009ca7ab49ea-22_1063_926_317_541}
17
- Write down the equation of the locus of \(C\) in the form
$$| z - w | = a$$
where \(w\) is a complex number whose real and imaginary parts are integers, and \(a\) is an integer.
17 - It is given that \(z _ { 1 }\) is a complex number representing a point on \(C\). Of all the complex numbers which represent points on \(C , z _ { 1 }\) has the least argument.
17
- Find \(\left| z _ { 1 } \right|\)
Give your answer in an exact form.
17
- (ii) Show that \(\arg z _ { 1 } = \arcsin \left( \frac { 6 \sqrt { 3 } - 2 } { 13 } \right)\)
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