Can magnitude of complex numbers raised to some power

[StephanJ]

Hey People just a general question

Is the following necessarily possible?

|z²³|=|z|²³

Where z is a complex number. I can't think of a reason why not but then again complex numbers have some subtle behaviours.

Thanks

 

[Hootenanny]

Welcome to Physics Forums.

Hey People just a general question

Is the following necessarily possible?

|z²³|=|z|²³

Where z is a complex number. I can't think of a reason why not but then again complex numbers have some subtle behaviours.

Thanks

If we take a look in polar form, we have

$$|z^{n}| = ||z|^ne^{in\cdot\text{arg}z}| = |z|^n|e^{in\cdot\text{arg}z}| = |z|^n$$

 

[StephanJ]

Haha I can't believe I didn't try polar form. Thanks for that