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Complex numbers

  1. Nov 23, 2008 #1
    we have z = 5+2i

    how do i find the following:

    |z|
    z-1


    i can do the basic operations (x, /, +, -) with complex numbers but i have no idea where to even start with these 2.
     
  2. jcsd
  3. Nov 23, 2008 #2
    For a complex number z=a+ib, the conjugate is defined as [itex]\bar z=a-ib[/itex]. |z| is the absolute value of z, the distance of z to the origin in the complex plane, and can be calculated as [itex]|z|^2=z\bar z=a^2+b^2[/itex]. [itex]z^{-1}[/itex] is the inverse of z, defined by the property that [itex]zz^{-1}=1[/itex], so [itex]z^{-1}=\frac{a-ib}{a^2+b^2}[/itex]
     
  4. Nov 23, 2008 #3
    set z=a+bi, then |z|=sqrt(a*a+b*b)...then you can do the first one.
    for the second one, it is 1/z.
    1/z=1/(5+2i)=(5-2i)/29
     
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