How do you find the norm of a complex vector

Question

How would I go about finding the norm of a complex vector, for instance:

$$\|(2x+3ix)+(3y+2iy)\|$$

Answer 1

I gather that you actually want $|2z+3iz|$, the modulus of this complex number. Since the modulus is multiplicative, that would be $$|2z+3iz| = |2+3i|\,|z|=\sqrt{2^2+3^2}|z|$$ You can simplify the square root. About $|z|$ we don't have any information.