Find the Norm [[1+i],[1-i],[1]]

Problem

‖[1+i],[1−i],[1]‖

Solution

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

∥v∥=√(,(∑_k=1^n)(|)*(z_k)|2)

2. Calculate the squared magnitude for each component by multiplying the component by its complex conjugate.

|1+i|2=(1+i)*(1−i)=1+1=2

|1−i|2=(1−i)*(1+i)=1+(−1)2=2

|1|2=1=1

3. Sum the squared magnitudes of all the components.

2+2+1=5

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

√(,5)

Final Answer

‖[1+i],[1−i],[1]‖=√(,5)

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