Respuesta :

DᴀʀᴋPᴀʀᴀᴅᴏx

let z be a complex number and z = x + iy

now, let's solve for 1/z

  • [tex] \dfrac{1}{z} [/tex]

  • [tex] \dfrac{1}{x + iy} [/tex]

  • [tex] \dfrac{1}{x + iy} \times \dfrac{ x - iy}{x - iy}[/tex]

  • [tex] \dfrac{x - iy}{ {x}^{2} - {i}^{2}y {}^{2} } [/tex]

  • [tex] \dfrac{x - iy}{ {x}^{2} + {y}^{2} } [/tex]

  • [tex] \dfrac{x}{ {x}^{2} + {y}^{2} } + i \dfrac{ - y}{ {x}^{2} + {y}^{2} } [/tex]

now, we can compare it with general form, where

  • [tex]a = \dfrac{x}{ {x}^{2} + {y}^{2} } [/tex]

  • [tex]b = \dfrac{ - y}{ {x}^{2} + {y}^{2} } [/tex]

In general form :

  • [tex] \dfrac{x}{ {x}^{2} + {y}^{2} } + i \dfrac{ - y}{ {x}^{2} + {y}^{2} } [/tex]

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