Verified answer

-1 + i√3 = 2 cis(⅔π)

z = (-1+sqrt(3)i)¹¹ = (2 cis(⅔π))¹¹ = 2¹¹ cis¹¹(⅔π) = 2¹¹ cis(²²∕₃π) = 2¹¹ cis(¹⁶∕₃π) = 2¹¹ cis(¹⁰∕₃π) = 2048 cis(⁴∕₃π)

θ = ⁴∕₃π

sqrt( (-1)^2 + (sqrt(3))^2 ) = sqrt( 1+3) = sqrt(4) = 2

(-1,sqrt(3)) lies in quadrant II

theta = tan^-1(-sqrt(3)/1) = -pi/3 or 2pi/3

z=[2(cos(2π/3)+isin(2π/3))]^11

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