Answer:
(D). [tex]\frac{\sqrt{2} }{8}[/tex] cis [tex]\frac{47\pi }{36}[/tex]
Step-by-step explanation:
cis [tex]\alpha[/tex] × cis [tex]\beta[/tex] = cis ( [tex]\alpha[/tex] + [tex]\beta[/tex] )
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[tex]\frac{\sqrt{6} }{6}[/tex] cis [tex]\frac{5\pi }{9}[/tex] × [tex]\frac{\sqrt{3} }{4}[/tex] cis [tex]\frac{3\pi }{4}[/tex] = ( [tex]\frac{\sqrt{6} }{6}[/tex] × [tex]\frac{\sqrt{3} }{4}[/tex] )[cis ( [tex]\frac{5\pi }{9}[/tex] + [tex]\frac{3\pi }{4}[/tex] )] = [tex]\frac{\sqrt{2} }{8}[/tex] cis [tex]\frac{47\pi }{36}[/tex]
