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a+bi algebraic alternating current analytic function angle argument axis circle circumference coefficients complex quantities complex variable conformal representation conjugate complex numbers conjugate systems constant convergent coordinates corresponding Cos2 cosec cosh 2y Cosine series coth curve derivative determine equal equation Euler's formulae exponential function expression factors Fourier's series function f(x Geometrical hence hyperbolic functions hyperbolic sine imaginary roots infinite number interval isin kx Cos px kx dx Laplace's equation Let us consider limit logarithm modulus multiplying nth root obtained odd function oosh parallel periodic function plane point representing Prom px dx qsoo ratio rational function real roots real variable reduces relation roots of unity satisfied sech Sin2 sinh Solve systems of isothermal tangent tanh theorem tion transformation trigonometric functions unity vanish z-plane