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Length of vector (1,i) ?

  1. Nov 22, 2012 #1
    I have a vector (1,i) and need to normalize it. I am being told that the answer is 1/(sqrt(2)) (1,i) but it seems clear to me that the vector's length is 0 and thus can't be normalized. What am i missing?
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  3. Nov 22, 2012 #2

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    Hi DocZaius! :smile:

    The length of a vector containing complex numbers is defined slightly different.

    From http://en.wikipedia.org/wiki/Norm_(mathematics):
    On an n-dimensional complex space ℂn the most common norm is
    $$\|\boldsymbol{z}\| := \sqrt{|z_1|^2 + \cdots + |z_n|^2}= \sqrt{z_1 \bar z_1 + \cdots + z_n \bar z_n}.$$
  4. Nov 22, 2012 #3
  5. Nov 24, 2012 #4


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    The absolute value |z| of a complex number z=a+ib is defined by ##|z|=\sqrt{a^2+b^2}##, or equivalently, by ##|z|=\sqrt{z^*z}##, where z*=a-ib is the complex conjugate of z.
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