Diketahui f(z) = -3z^2
- Ubahlah ke bentuk f(z) = u(x,y)+iv(x,y) ; z=x+yi
- Buktikan f'(z) = -6z dengan f'(z) = ux(x,y) + ivx(x,y)
Penyelesaian:
-
Ubahlah ke bentuk f(z) = u(x,y)+iv(x,y) ; z=x+yi
f(z) = -3z^2 = -3 (x+yi)^2 = -3(x^2+2xyi-y^2)
f(z) = -3x^2-6xyi-3y^2
Maka:
f(z) = u(x,y)+iv(x,y)
f(z) = (-3x^2 +3y^2) + i(-6xy)
f(z) = -3(x^2 -y^2) + i(-6xy) -
Buktikan f'(z) = -6z dengan f'(z) = ux(x,y) + ivx(x,y)
f(z) = u(x,y)+iv(x,y)
f(z) =-3x^2 +3y^2 + i(-6xy)Maka:
u(x,y) = -3x^2 +3y^2; ux(x,y) = -6x
v(x,y) =-6xy; vx(x,y) = -6ySehingga didapat:
f'(z) = ux(x,y) + ivx(x,y)
f'(z) = (-6x) + i (-6y)
f'(z) = -6 (x+yi)
f'(z) = -6zTerbukti f'(z) = -6z dengan f'(z) = ux(x,y) + ivx(x,y)