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Complex Numbers - Coggle Diagram

- - - - In Im(b)'s case "b" is the coeficent of i, which is √-1
  - - - therefore
        
        we can make the complex plane
        
        Complex numbers that are neither real nor purely imaginary (a and b are both not 0) lie in one of the four quadrants.
        
        The origin (0,0) lies on both axes. It corresponds to z=0, a real number
        
        All purely imaginary numbers with a=0 lie on the imaginary axis
        
        All real numbers with b=0 lie on the real axis.
        
        because
        
        it would look like this: a + 0*1= a
        
        1 more item...
- - - - what is it?
        
        the length of a vector
      - the formula for it
        
        which is coming from
        
        it is hypothenus
        
        Properties of Modulus
        
        How you do it?
        
        without the imaginary part
    - - what is it?
        
        It is the teta angle, which is between vector and the x-axsis
        
        in other words
        
        how do we find the theta?
        
        If we put the theta angle in a triangle, we can find the theta from the tanjant (sin/cos)
      - Note That
- - - - On this complex plane the z= a +bi complex number was shown
      - the modulus of it is |z| = √a2 + b2
        
        in this case it is represented buy r
      - the ϑ is the argument of the vector
        
        arg(z) = ϑ