Step-by-step explanation:
[tex] \frac{2 + 3i}{4 - 5i} [/tex]
[tex] \frac{(2 + 3i)(4 + 5i)}{(4 - 5i)(4 + 5i)} [/tex]
[tex] \frac{8 + 10i + 12i + 15 {i}^{2} }{16 - 25 {i}^{2} } [/tex]
[tex] \frac{8 + 22i + 15( -1 )}{16 - 25 ( - 1)} [/tex]
[tex] \frac{8 - 15 + 22i}{16 + 25} [/tex]
[tex] \frac{ - 7 + 22i}{41} [/tex]
So, a= -7
b= 22
c= 41
