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

Problem

‖[2−i],[3+i],[3+4*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 the first component (z_1)=2−i

|2−i|2=2+(−1)2=4+1=5

3. Calculate the squared magnitude for the second component (z_2)=3+i

|3+i|2=3+1=9+1=10

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

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

5. Sum the squared magnitudes.

5+10+25=40

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

√(,40)=√(,4⋅10)=2√(,10)

Final Answer

‖[2−i],[3+i],[3+4*i]‖=2√(,10)

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