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  • Mathematics
    Algebra: Complex Numbers
    • Vectors
      • Matrices
        • Vector Space
          • Algebra
            • Factorization
            • Complex Numbers
            • Quadratic Equation
            • Cubic Equation
            • Polynomial Roots
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              Equations
          • Calculus
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              • Analytic Geometry
                • Statistics & Probability
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                    • Special Functions

                      Complex Number Arithmetic

                      You can enter each of the the complex numbers z1,2 in either the "standard" form z = x + y i, where x is its real part and y is imaginery part, or
                      in its "phasor" (exponential) form z = | z | e φ , where | z | is its modulus and φ is its phase.

                      First complex numberz1 = + i
                      its phasor form= ⋅ e i
                      Second complex numberz2 = + i
                      its phasor form= ⋅ e i

                      Conjugatez1 = 0
                      z2 = 0
                      Modulus| z1 | = 0
                      | z2 | = 0
                      Aditionz1 + z2 = 0
                      Subtractionz1 - z2 = 0
                      Multiplicationz1 ⋅ z2 = 0
                      Divisionz1z2 = 0
                      Square root
                      √
                       z1 
                      =
                      0
                      √
                       z2 
                      =
                      0
                      Exponentialez1 = 1
                      Powerz1z2 = 1
                      Natural Logarithm (e log(z) = z)log(z1) = -Infinity
                      Sinesin(z1) = 0
                      Cosinecos(z1) = 1

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