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

Problem

‖[2+3*i],[4−i],[3+2*i]‖

Solution

1. Identify the formula for the Euclidean norm (also known as the L2 norm) of a complex vector, which is the square root of the sum of the squared magnitudes of its components.

‖v‖=√(,|(z_1)|2+|*(z_2)|2+|(z_3)|2)

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

|2+3*i|2=2+3=4+9=13

|4−i|2=4+(−1)2=16+1=17

|3+2*i|2=3+2=9+4=13

3. Sum the squared magnitudes of the components.

13+17+13=43

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

√(,43)

Final Answer

‖[2+3*i],[4−i],[3+2*i]‖=√(,43)

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