Math Help - Complex number plane multiplication

We know that multiplying the plane of complex numbers by a constant complex number u multiplies all distances by the absolute value of u.


Assuming that u is not equal to 1, and hence that uz is not equal to z when z is not equal to 0, deduce that multiplication by u is a rotation.

Originally Posted by meggnog

We know that multiplying the plane of complex numbers by a constant complex number u multiplies all distances by the absolute value of u.


Assuming that u is not equal to 1, and hence that uz is not equal to z when z is not equal to 0, deduce that multiplication by u is a rotation.

Let

and .


Therefore

.


Since the angle has changed, that means you have a rotation.