Answer:
[tex]a=13\\ \\b=7-4i[/tex]
Step-by-step explanation:
Consider the expression in the brackets:
[tex]\dfrac{3+2i}{2-3i}+\dfrac{5-i}{2+3i}[/tex]
Simplify it:
[tex]\dfrac{3+2i}{2-3i}+\dfrac{5-i}{2+3i}\\ \\=\dfrac{(3+2i)(2+3i)+(5-i)(2-3i)}{(2-3i)(2+3i)}\\ \\=\dfrac{6+9i+4i+6i^2+10-15i-2i+3i^2}{2^2-(3i)^2}\\ \\=\dfrac{16-4i+9i^2}{4-9i^2}\\ \\=\dfrac{16-4i-9}{4-9(-1)}\\ \\=\dfrac{7-4i}{13}[/tex]
So,
[tex]a=13\\ \\b=7-4i[/tex]
