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Question

Consider the equation z^{11} = (1 + \sqrt{3}\, i). Find the value of z which satisfies this equation and which has the second smallest positive argument \theta, 0 < \theta < 2\pi. Express your answer as z = r e^{i \theta} where
r = and \theta =

Answer 1

Assuming "z" is a complex number:

z¹¹ = |z|¹¹ (cos 11θ + i sin 11θ)

Base on the conditions:

cos 11θ + i sin θ = 1 + i√3

Therefore:

cos 11θ = 1

θ = 0.

If θ = 0, then sin 11θ = 1 which is not √3.