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 L^2 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=a^2+b^2

3. Compute the first component's squared magnitude:

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

4. Compute the second component's squared magnitude:

|4−2*i|^2=4^2+(−2)^2=16+4=20

5. Compute the third component's squared magnitude:

|0−4*i|^2=0^2+(−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)

Want more problems? Check here!