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

Problem

‖[4−i],[4−2*i],[2+2*i],[3−3*i]‖

Solution

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

∥v∥=√(,(∑_i=1^n)(|)*(z_i)|2)

2. Calculate the squared magnitude |z|2 for each component by summing the squares of the real and imaginary parts, using |a+b*i|2=a2+b2

|4−i|2=4+(−1)2=16+1=17

|4−2*i|2=4+(−2)2=16+4=20

|2+2*i|2=2+2=4+4=8

|3−3*i|2=3+(−3)2=9+9=18

3. Sum the squared magnitudes of all components.

17+20+8+18=63

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

√(,63)=√(,9⋅7)=3√(,7)

Final Answer

‖[4−i],[4−2*i],[2+2*i],[3−3*i]‖=3√(,7)

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