Question

Sa se rezolve, in multimea numerelor complexe, ecuatiile:
a) x² = -9
b) x² - 8x + 25 = 0
c) x² - 2x + 4 = 0
d) x² + 2x + 2 = 0
e) x la a 4a = 16

Answer 1

$a)x^{2} =-9;x=3i;x=-3i \\ b) x^{2} -8x+25=0$
Δ=$64-100=-36$
$x_{1} =\frac{8-6i}{2}=4-3i \\ x_{2}=4+3i$
$c) x^{2} -2x+4=0$
Δ=$4-16=-12 \\ x_{1}= \frac{2-2i \sqrt{3} }{2}=1-i \sqrt{3} \\ x_{2}=1+i \sqrt{3}$
d)$x^{2} +2x+2=0$
Δ=4-8=-4
$x_{1} =\frac{-2-2i}{2}= -1-i \\ x_{2}=-1+i$
$e)x^4=16 \\ x_{1}=2; x_{2}=-2; x_{3}=2i; x_{4}=-2i$