1/2 +1/2 i-i 1/2-1/2i (1/2-1/2i )(1/2-1/2i)
1-: f(1/2 +1/2 i) = ......................= .............. =....................................
(1/2+1/2i 1/2+1/2i (1/2+1/2i)(1/2-1/2i)
(1/2 -1/2i)² (1/2)²-2x(1/2)(1/2i)+(1/2i)²
=.............................................= ........................................
(1/2)² - (1/2i)² 1/4- (1/4)(-1)
1/4- (1/2)i + (1/4)(-1) 1/4+1/4 -1/2 i
=.......................................=..................................= (1/2-1/2i)x2 =1 -i
1/4+1/4 1/2
3-5i-i 3-6i (3-6i)(3+5i) 9+15i-18i-30(-1)
f(3-5i)=............. =................=........................=............................
3-5i 3-5i (3-5i)(3+5i) 3²-(5i)²
9+30-3i 39-3i 39-3i 39 3
=.....................= ...................=.............= ...... - ..... i
9-25(-1) 9+25 34 34 34
2) resoudre l'equation :a) f(z)= - 2i
z-i i i(1-2i)
............. =-2i⇔ z-i= (-2i)z ⇔z+(2i)z=i ⇔(1+2i)z=i ⇔ z=..............=....................
z 1+2i (1+2i)(1-2i)
i-2(-1) i+2 i+2 i+2
............... =............ =............. =.........=(1/5) i+ 2/5
1² - (²2i) 1-4(-1) 1+4 5
b) f(z)= 3-5i
z-i
..... = 3-5i ⇔ z-i = z(3-5i) ⇔z-(3-5i)z = i ⇔(1-(3-5i))z=i ⇔(5i-2)z=i
z
i i(5i+2) 5(-1) +2i 2i-5 2i-5
z =..............=......................=................... =.....................=...................
5i-2 (5i-2)(5i+2) (5i)²- 2² 25(-1) -4 -29
z =(-2/29)i +5/29
x +iy-i
3) a)exprimer: f(z)=................
x +iy
