(a + bi)(2 + 3i) - i = (-11 + 5i)(1 - i)
(a + bi)(2 + 3i) - i = -11 + 11i + 5i - 5i²
(a + bi)(2 + 3i) - i = -6 + 16i
(a + bi)(2 + 3i) = -6 + 17i
[tex]a+bi=\frac{-6+17i}{2+3i}[/tex]
[tex]a+bi=\frac{(-6+17i)(2-3i)}{(2+3i)(2-3i)}[/tex]
[tex]a+bi=\frac{-12+18i+34i-51i^2}{4+9}[/tex]
[tex]a+bi=\frac{39+52i}{13}[/tex]
a + bi = 3 + 4i
a = 3, b = 4
