Question

Given the following vector;
<2/5*sqrt(2), 2i/5*sqrt(2), -0.5, -i/2> normalize the vector.

Answer 1

multiply each component by its complex conjugate, sum the result, and take the square root. You will have a positive real number.

Answer 2

divide the whole thing by that resulting real number (the magnitude) to normalize the vector

Answer 3

What do you mean by their complex conjugate.

Answer 4

any complex number can be written\[z=a+bi\]and has complex conjugate\[z^*=a-bi\]notice that the product \[zz^*=a^2+b^2\in\mathbb R\]so the result is always rel

Answer 5

real*

Answer 6

Can you give example of a set of another vector and point out their conjugate

Answer 7

say we had\[z=\langle5,2+3i,-\sqrt2 i\rangle\]then the complex conjugate (or Hermitian conjugate) is\[z^*=\begin{bmatrix}5\\2-3i\\\sqrt2i\end{bmatrix}\]

Answer 8

the sign on the imaginary part flips, and we take the transpose of the matrix so we can take the product and get a real number