Answer:
C
Step-by-step explanation:
reciprocal of z=1/z
[tex]z=2(cos \frac{\pi }{4} +i sin\frac{\pi }{4} )=2e ^{i \frac{\pi } {4}\\\frac{1}{z}=\frac{1}{2e^{i \frac{\pi}{4} } }\\\frac{1}{z} =\frac{1}{2} e^{-i\frac{\pi}{4} } \\\frac{1}{z} (cos\frac{\pi}{4} -isin\frac{\pi}{4} ) \\\frac{1}{z}=\frac{1}{2} (\frac{\sqrt{2} }{2} -\frac{\sqrt{2} }{2} )\\\frac{1}{z} =\frac{\sqrt{2} }{4} -i \frac{\sqrt{2 } }{4}[/tex]
