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

Problem

‖[2+0*i],[3−4*i],[4+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 √(,|(z_1)|^2+|*(z_2)|^2+⋯+|(z_n)|^2)

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

3. Compute the squared magnitude for the first component (z_1)=2+0*i

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

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

|3−4*i|^2=3^2+(−4)^2=9+16=25

5. Compute the squared magnitude for the third component (z_3)=4+3*i

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

6. Sum the squared magnitudes of all components.

4+25+25=54

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

√(,54)=√(,9⋅6)=3√(,6)

Final Answer

‖[2+0*i],[3−4*i],[4+3*i]‖=3√(,6)

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