Question

A complex number, (a + bi), multiplied by (2 + 3i) and added to -i gives the product of (-11 + 5i) and (1 – i). a = and b =

Answer 1

(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
$a+bi=\frac{-6+17i}{2+3i}$
$a+bi=\frac{(-6+17i)(2-3i)}{(2+3i)(2-3i)}$
$a+bi=\frac{-12+18i+34i-51i^2}{4+9}$
$a+bi=\frac{39+52i}{13}$
a + bi = 3 + 4i

a = 3, b = 4