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complex number

if any complex number, w, multiplies by another complex number, would it always perform some sort of rotation about the origin?
Original post by Iconic_panda
if any complex number, w, multiplies by another complex number, would it always perform some sort of rotation about the origin?


Yes.

This is easy to see from the polar form. Denote z1=Reiθz_1=Re^{i\theta} and z2=Peiωz_2 = Pe^{i \omega}. Then the complex number

w=z1z2=RPei(θ+ω)w = z_1z_2 = RPe^{i(\theta + \omega)}

clearly has the argument is displaced by an angle ω\omega from θ\theta in z1z_1 (and of course, the magnitude is affected too granted P≠1P \neq 1)
(edited 5 years ago)
ohh thats smart thanks!
Original post by RDKGames
Yes.

This is easy to see from the polar form. Denote z1=Reiθz_1=Re^{i\theta} and z2=Peiωz_2 = Pe^{i \omega}. Then the complex number

w=z1z2=RPei(θ+ω)w = z_1z_2 = RPe^{i(\theta + \omega)}

clearly has the argument is displaced by an angle ω\omega from θ\theta in z1z_1 (and of course, the magnitude is affected too granted P≠1P \neq 1)

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