№2;4. комплексные числа

2. z1+2z2=1-4i+2(2-3i)=1+4-4i-6i=5-10i [latex] \frac{z_{1} }{z_{2}} = \frac{1-4i}{2-3i}= \frac{(1-4i)(2+3i)}{(2-3i)(2+3i)}= \frac{2+3i+6i+12}{4+9}=\frac{14+9i}{13}= \frac{14}{13} + \frac{9}{13} i[/latex] 4.[latex]z= \frac{i}{4+7i} = \frac{i(4-7i)}{(4+7i)(4-7i)} = \frac{4i+7}{16+49}= \frac{7+4i}{65}= \frac{7}{65}+ \frac{4}{65}i [/latex]