Find the Norm [[4+2i],[4+0i],[1-3i]]

Problem

‖[4+2*i],[4+0*i],[1−3*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_3)]^T which is defined as √(,|(z_1)|^2+|*(z_2)|^2+|(z_3)|^2)

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

3. Compute the first component's squared magnitude: |4+2*i|^2=4^2+2^2=16+4=20

4. Compute the second component's squared magnitude: |4+0*i|^2=4^2+0^2=16+0=16

5. Compute the third component's squared magnitude: |1−3*i|^2=1^2+(−3)^2=1+9=10

6. Sum the squared magnitudes: $20 + 16 + 10 = 46$.

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

Final Answer

‖[4+2*i],[4+0*i],[1−3*i]‖=√(,46)

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