31. In that case, the imaginary part of the result is a Hilbert transform of the real part. 32. The mapping is non-analytic because its real and imaginary parts do not obey the Cauchy Riemann equations. 33. The imaginary part arises from kinetic inductance. 34. The standard representation for complex numbers is as the sum of a real part and an imaginary part . 35. The modulus of a torus can be captured by a single complex number ? with positive imaginary part . 36. When the imaginary parts of any eigenvalues ( shown in cyan ) are non-zero, the bike exhibits oscillation. 37. Are they real or imaginary parts ? 38. The thick green line indicates the real part of the function, and the thin red line the imaginary part . 39. Oscillations are present when poles with real part equal to zero have an imaginary part not equal to zero. 40. For a fixed value of ? the potential is presented upwards against the real and imaginary parts of ?.
