The principle value of the \[\arg \,(z)\] and \[|z|\] of the complex number \[z=1+\cos \left( \frac{11\pi }{9} \right)+i\sin \left( \frac{11\pi }{9} \right)\] are respectively.

\[\frac{2\pi }{9},2\cos \left( \frac{7\pi }{18} \right)\]

\[\frac{11\pi }{8},\,2\cos \left( \frac{\pi }{18} \right)\]

\[-\frac{7\pi }{18},-2\cos \left( \frac{11\pi }{18} \right)\]

\[-\frac{\pi }{9},-2\cos \left( \frac{\pi }{18} \right)\]

The principle value of the \[\arg \,(z)\] and \[|z|\] of the complex n

1.	The principle value of the \[\arg \,(z)\] and \[\|z\|\] of the complex number \[z=1+\cos \left( \frac{11\pi }{9} \right)+i\sin \left( \frac{11\pi }{9} \right)\] are respectively.
A.	\[\frac{11\pi }{8},\,2\cos \left( \frac{\pi }{18} \right)\]
B.	\[-\frac{7\pi }{18},-2\cos \left( \frac{11\pi }{18} \right)\]
C.	\[\frac{2\pi }{9},2\cos \left( \frac{7\pi }{18} \right)\]
D.	\[-\frac{\pi }{9},-2\cos \left( \frac{\pi }{18} \right)\]
Answer» C. \[\frac{2\pi }{9},2\cos \left( \frac{7\pi }{18} \right)\]

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The principle value of the \[\arg \,(z)\] and \[|z|\] of the complex number \[z=1+\cos \left( \frac{11\pi }{9} \right)+i\sin \left( \frac{11\pi }{9} \right)\] are respectively.

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