Find the Norm [[0+0i],[2-3i],[1+2i],[1+0i]]

Problem

‖[0+0*i],[2−3*i],[1+2*i],[1+0*i]‖

Solution

1. Identify the formula for the Euclidean norm (also known as the L2 norm) of a complex vector v=[(z_1),(z_2),…,(z_n)]T which is ∥v∥=√(,(∑_k=1^n)(|)*(z_k)|2)

2. Calculate the squared magnitude of each complex component using the formula |a+b*i|2=a2+b2

3. Evaluate the squared magnitude for the first component (z_1)=0+0*i

|0+0*i|2=0+0=0

4. Evaluate the squared magnitude for the second component (z_2)=2−3*i

|2−3*i|2=2+(−3)2=4+9=13

5. Evaluate the squared magnitude for the third component (z_3)=1+2*i

|1+2*i|2=1+2=1+4=5

6. Evaluate the squared magnitude for the fourth component (z_4)=1+0*i

|1+0*i|2=1+0=1

7. Sum the squared magnitudes of all components:

0+13+5+1=19

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

√(,19)

Final Answer

‖[0+0*i],[2−3*i],[1+2*i],[1+0*i]‖=√(,19)

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