Question

Scrieți sub forma algebrica următoarele nr complexe
2+5i supra 1-i +2-5i supra 1+i
1 supra (1+3i)(2-i)

Answer 1

1) $\frac{2+5i}{1-i}+ \frac{2-5i}{1+i}=\frac{(2+5i)(1+i)}{(1-i)(1+i)}+ \frac{(2-5i)(1-i)}{(1+i)(1-i)}= \frac{2+2i+5i+5i^2+2-2i-5i+5i^2}{1-i^2}=$$\frac{4-10}{2}=-3.$
2) $\frac{1}{(1+3i)(2-i)}= \frac{1}{2-i+6i-3i^2}= \frac{1}{2+5i-3(-1)}= \frac{1}{5(1+i)}= \frac{1-i}{5(1+i)(1-i)}= \frac{1-i}{5(1-(i)^2)}$=$\frac{1-i}{5(1+1)}= \frac{1-i}{10}= \frac{1}{10}- \frac{1}{10}i.$