Răspuns:
Explicație pas cu pas:
1
z=8+6i
a)(8+6)²=14²=196
b)opusul lui z=-8+6i
conjugatul lui z=8+6i
c)IzI=√R²+I²=√64+36=√100=10
2
z1=1-3i z2=2+i
a)z1+3z2=1-3i+6+3i=7
b)z1·z2=(1-3i)(2+i)=2-6i+i+3=5-5i
c)z1/z2=a+bi
(1-3i)/(2+i)=(1-3i)·(2-i)/(4+1)=(2-6i-i+3)/5=(5-7i)/5
⇒a=1 b=-7/2
3
2z+zbarat=9+2i
2(a+bi)+a-bi=9+2i
2a+2bi+a-bi=9+2i
3a+bi=9+2i ⇒a=3 si b=1
b)x²-2x+5=0
x1,2=1±√1-5=1±2i x1=1+2i x2=1-2i
c)x1=3-i x2=3+i
x1+x2=6 x1x2=9+1=10
x²-6x+10=0
