(Cosθ + i Sinθ)n = Cos nθ + i Sin nθ
Take a fixed complex number on the unit circle
z = Cosθ + i Sinθ |z| = 1
Consider multiples of z by a real, positive number r.
r z = r (Cosθ + i Sinθ) |r z| = r |z| = r
As r increases from 1, point moves out along the ray with tail at the origin and passes through the point z.
As r decreases from 1 to zero, point moves inward along the same way toward the origin. The modulus of the point is r. We call the angle θ which this ray makes with the x-axis, the argument of the number z. All the numbers rz have the same argument.
arg rz = θ
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