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Multiple choice
On the Argand diagram, what is the geometric effect of multiplying a complex number
z
z
z
by
e
i
θ
e^{i\theta}
e
i
θ
?
It moves
z
z
z
one unit to the right along the real axis
It scales the modulus of
z
z
z
by a factor of
θ
\theta
θ
while keeping its angle fixed
It rotates
z
z
z
counterclockwise by angle
θ
\theta
θ
without changing its distance from the origin
It reflects
z
z
z
across the real axis
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