Complex numbers

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  • Imaginary numbers
    • i=sqrt(-1) i^2=-1 i^3=-I i^4=1
    • Complex number= real number+ imaginary number z=a+bi
      • x=a and y=b
        • z* is z reflected in the real axis
          • Complex conjugate z*=a-bi
            • z+z*=2a       z-z*=2bi zxz*=a^2+b^2
            • 0=x^2-(2a)x+(a^2+b^2)
    • Complex conjugate z*=a-bi
      • z+z*=2a       z-z*=2bi zxz*=a^2+b^2
      • 0=x^2-(2a)x+(a^2+b^2)

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