Question

(1+2i) (2+3i) divided by (2+i) express it in the form of a+bi​

Answer 1

Answer:

$\frac{(1 + 2i)(2 + 3i)}{(2 + i)} \\ \\ = \frac{1(2 + 3i) + 2i(2 + 3i) }{(2 + i)} \\ \\ = \frac{2 + 3i+ 4i + 6 {i}^{2} }{(2 + i)} \\ \\ = \frac{2 + 7i + 6 ( - 1) }{(2 + i)} \\ \\ = \frac{2 + 7i - 6 }{(2 + i)} \\ \\ = \frac{ 7i - 4}{(2 + i)} \\ \\ = \frac{ (7i - 4) \times (2 - i)}{(2 + i) \times (2 - i)} \\ \\ = \frac{ 7i (2 - i) - 4(2 - i)}{(2)^{2} - i ^{2} } \\ \\ = \frac{ 14i - 7i^{2} - 8 + 4 i}{4 - ( - 1)} \\ \\ = \frac{ 18i - 7( - 1) - 8 }{4 + 1} \\ \\ = \frac{ 18i + 7 - 8 }{5} \\ \\ = \frac{ 18i - 1 }{5} \\ \\ = \frac{ - 1 + 18i}{5} \\ \\ = \frac{ - 1}{5} + \frac{18i}{5} \\ \\ \purple{ \fbox{ = - \frac{ 1}{5} + \frac{18}{5}i \implies \: a + bi}}$