Exprimarea lui z=-5 in functie de argumentul redus
z=5*(cosπ+i sinπ)
Cazul general
Arg z={π+2kπ}
z=5*(cos((2k+1)π+i sin (2k+1))
b) z=l z l*(cosФ+i inФ)
l zl=√a²+b²=√0²+9=3 unde a= Re z si b=Im z
cos ∅=0/3=0
sin∅=-3/3=-1
Ф=3π/2
argumentul redus
z=3*(cos 3π/2+isin 3/2π)
Cazul general
Arg z= {3π/2+2kπ}=={π*(3/2+2k)}
z=3*[cos(3/2+2k)π =isin(3/2+2kπ)]
c) l z l=√4+4=2*√2
argumentul redus
cosФ=2/2*√2=√2/2=>
sin Ф=-2/2√2= - √/2
sinusul negati, cos-ul pozitiv =. esti in cadran4
Ф=7π/4
z=2*√2*[cos7π/4+isin7π/4)
Cazul general
Arg z={7π/4+2kπ}
z=2*√2*[cos(7π/4+2kπ)+isin(7π/4+2kπ)]
d)l z l=√9+16=5
cosФ=3/5 Ф=arccos 3/5
sinФ=4/5 Ф arcsin 3/5) Ф∈primul cadran
z in functie deargumentul redus
z=5*(cos(arc cos 3/5)+i(sin(sin arcsin 3/5)}
cazul genral
z=5*(cos(arc cos3/5+2kπ)+isin (arc sin 3/5+2kπ)
