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

Problem

‖[3−2*i],[3−2*i],[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_3)]T which is ∥v∥=√(,|(z_1)|2+|*(z_2)|2+|(z_3)|2)

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

3. Compute the magnitude for the first component (z_1)=3−2*i

|3−2*i|2=3+(−2)2=9+4=13

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

|3−2*i|2=3+(−2)2=9+4=13

5. Compute the magnitude for the third component (z_3)=0−i

|0−i|2=0+(−1)2=0+1=1

6. Sum the squared magnitudes:

13+13+1=27

7. Take the square root of the sum to find the norm:

√(,27)=√(,9⋅3)=3√(,3)

Final Answer

‖[3−2*i],[3−2*i],[−i]‖=3√(,3)

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