Explicație pas cu pas:
a)
[tex] \frac{1 + 2x}{1 - 2i} + \frac{2 + y}{1 + 2i} = i \\ [/tex]
[tex](1 + 2x)(1 + 2i) + (2 + y)(1 - 2i) = i(1 + 2i)(1 - 2i) \\ [/tex]
[tex]1 + 2i + 2x + 4xi + 2 - 4i + y - 2yi = i(1 + 4) \\ [/tex]
[tex](2x + y + 3) + i(4x - 2y - 2) = 0 + 5i \\ [/tex]
[tex]\left \{ {{2x + y + 3 = 0} \atop {4x - 2y - 2 = 5}} \right. \\ \left \{ {{4x + 2y + 6 = 0} \atop {4x - 2y - 2 = 5}} \right. \\[/tex]
[tex]8x + 4 = 5 \\ 8x = 1 = > x = \frac{1}{8} \\ y = - 3 - \frac{2}{8} = - \frac{26}{8} \\ = > y = - \frac{13}{4} [/tex]
b) (1 - i√3)³ = a + bi
1³ - 3×1²×i√3 + 3×1×(i√3)² - (i√3)³ = a + bi
1 - 3i√3 - 9 + 3i√3 = a + bi
-8 = a + bi
-8 + 0i = a + bi
→
a = -8
b = 0
