Answer:a = 13 and b = 12-5iStep-by-step explanation:We need a common denominator3+2i 5-i---------- + ---------3-2i 2+3i (3+2i) (2+3i) (5-i)(3-2i)------------------ + --------------------(3-2i) (2+3i) (2+3i) (3-2i) Foil the numerators6 +4i+9i+6i^2 +15-3i-10i+2i^2 ------------------ -------------------- (2+3i) (3-2i) Combine like terms21 +8i^2 ------------------ (2+3i) (3-2i) We know that i^2 = -121 +8(-1) ------------------ (2+3i) (3-2i) 21 -8 ------------------ (2+3i) (3-2i) 13 ------------------ (2+3i) (3-2i) Foil the denominator13---------------6 +9i -4i -6i^2Combine like terms13----------------6+ 5i -6(-1)13----------12 +5iWe know have13-------------12 + 5iMultiply by the conjugate13 ( 12-5i)------------- * -------------12 + 5i 12 -5i13 (12-5i)--------------144 +2513(12-5i)-------------16912-5i------------13The parentheses are (12-5i)/13We need the reciprocal to make the equation become 1which is 13/ 12-5ia = 13 and b = 12-5i