Question

Determinați partea reala a numarului complex z=3+i/1-3i

Answer 1

   
[tex]\displaystyle\\ z= \frac{3+i}{1-3i} ~~~\text{ Rationalizam fractia. Atentie! }~ i^2=-1 \\ \\ z= \frac{3+i}{1-3i} = \frac{(3+i)((1+3i)}{(1-3i)(1+3i)} = \frac{3+i+9i+3i^2}{1-9i^2} = \\ \\ = \frac{3+i+9i-3}{1+9} = \frac{3-3+i+9i}{1+9} =\frac{0+10i}{10} =\boxed{0+i} = \boxed{i} \\ \\ \text{Numarul "complex" nu are parte reala. }\\ \text{Putem spune ca partea reala = 0.}[/tex]