Find the Norm [[0+3i],[4+3i],[2+0i],[2-3i]]

Problem

‖[0+3*i],[4+3*i],[2+0*i],[2−3*i]‖

Solution

1. Identify the formula for the Euclidean norm (also known as the L^2 norm) of a complex vector v=[(z_1),(z_2),…,(z_n)]^T which is given by √(,(∑_k=1^n)(|)*(z_k)|^2)

2. Calculate the squared magnitude |z|^2 for each component by using the formula |a+b*i|^2=a^2+b^2

3. Compute the squared magnitude of the first component:

|0+3*i|^2=0^2+3^2=9

4. Compute the squared magnitude of the second component:

|4+3*i|^2=4^2+3^2=16+9=25

5. Compute the squared magnitude of the third component:

|2+0*i|^2=2^2+0^2=4

6. Compute the squared magnitude of the fourth component:

|2−3*i|^2=2^2+(−3)^2=4+9=13

7. Sum the squared magnitudes of all components:

9+25+4+13=51

8. Take the square root of the sum to find the final norm.

Final Answer

‖[0+3*i],[4+3*i],[2+0*i],[2−3*i]‖=√(,51)

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