Question

Determinați perechea (a,b) de numere reale, știind că 1 + (a+b)·i = a + 3i, unde i ∈ C, $i^{2}$ = -1.

Answer 1

 

$\displaystyle\\1+(a+b)\cdot i=a+3i\\\text{Facem egalitate intre partea reala a fiecarui numar complex.}\\\text{Facem egalitate intre coeficientii partii imaginare a fiecarui numar complex.}\\\\a=1\\a+b=3\\\\1+b=3\implies~b= 3-1=2\\\\\bf~Solutia\!:\\\\\boxed{\bf~a=1~si`b=2}$