Question

Express the complex number z = 5+i/ 2+3i in form of a a+ib

Answer 1

$z = \frac{5 + i}{2 + 3i} \\ z = \frac{5 + i}{2 + 3i} \times \frac{2 - 3i}{2 - 3i} \\ z = \frac{10 - 15i + 2i - 3 {i}^{2} }{ {2}^{2} - ( {3i})^{2} } \\ z = \frac{10 - 13i + 3}{4 + 9} \\ z = \frac{13 - 13i}{13} \\ z = 1 - i \\ z = 1 + i.( - 1)\\ here \: \: \: \: a = 1 \: \: \: \: \: \: b = - 1$