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

Problem

‖[4+3*i],[4−2*i],[0−4*i]‖

Solution

1. Identify the formula for the Euclidean norm (also known as the L2 norm) of a complex vector v=[(z_1),(z_2),(z_3)]T which is ∥v∥=√(,|(z_1)|2+|*(z_2)|2+|(z_3)|2)

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

3. Compute the first component's squared magnitude:

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

4. Compute the second component's squared magnitude:

|4−2*i|2=4+(−2)2=16+4=20

5. Compute the third component's squared magnitude:

|0−4*i|2=0+(−4)2=0+16=16

6. Sum the squared magnitudes:

25+20+16=61

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

Final Answer

‖[4+3*i],[4−2*i],[0−4*i]‖=√(,61)

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