Question 1208305
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Answer: <font color=red>True</font>


Work Shown


z = sin(x) + i*cos(x)
z = cos(90-x) + i*sin(90-x) ......... use <a href="https://tutorial.math.lamar.edu/pdf/Trig_Cheat_Sheet_Reduced.pdf">trig identities</a>
z^9 = cos(9*(90-x)) + i*sin(9*(90-x))   ................   <a href="https://math.libretexts.org/Courses/Rio_Hondo/Math_175%3A_Plane_Trigonometry/06%3A_The_Polar_System/6.05%3A_De_Moivre's_and_the_nth_Root_Theorem">De Moivre's Theorem</a>
z^9 = cos(810 - 9x) + i*sin(810 - 9x)
z^9 = cos(810)cos(9x) + sin(810)sin(9x) + i*( sin(810)cos(9x) - cos(810)sin(9x) ) .... use two more trig identities
z^9 = 0*cos(9x) + 1*sin(9x) + i*( 1*cos(9x) - 0*sin(9x) )
z^9 = sin(9x) + i*cos(9x)
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