Question

Numere complexe
vreau rezolvare pas cu pas nu doar răspunsul
Mulțumesc!​

Answer 1

Răspuns:

b) s = 5

Explicație pas cu pas:

Notam cu x = Re(z) si y = Im(z)

$z = x + yi\\\\z - 4 = x - 4 + yi\\\\lzl = lz-4l\\\\\sqrt{x^2 + y^2} } = \sqrt{(x-4)^2 + y^2} }\\\\x^2 + y^2 = (x-4)^2 + y^2\\\\x^2 - (x-4)^2 = 0 \\\\(x + x - 4)(x - x + 4) = 0\\\\4(2x - 4) = 0\\\\x = 2$

$z = 2 + yi\\\\z^2 = -5 + 12i\\\\(2 + yi)^2 = -5 + 12\\\\4 + 4yi - y^2 = -5 + 12i\\\\\left \{ {{\Big{4 - y^2 = -5}} \atop {\Big{4yi = 12i}}} \right. \\\\\\\left \{ {{\Big{y^2 = 9}} \atop {\Big{y = 3}}} \right.$

$y = 3\\\\s = Re(z) + Im(z) = 2 + 3 = 5$