FLC OF A C550 CITATION STEEPENED THEIR BANK IN RESPONSE TO A TCASII RA; AND COMPLYING WITH AN ARTCC CTLR HDG CHANGE FOR TFC SEPARATION.

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AT APPROX XA30 NEAR VANDALIA; IL; WE WERE GIVEN A DSCNT TO FL280. AT THE TIME WHEN WE DSNDED THROUGH APPROX FL300; ZKC TOLD US TO MAKE AN IMMEDIATE L TURN WITHOUT DELAY TO A 270 DEG HDG DUE TO TFC. (AT THIS TIME WE WERE DIRECT TO MOLINE; IL; ON ABOUT A 320 DEG HDG.) I IMMEDIATELY BANKED THE CESSNA CITATION 650 TO ABOUT 40-45 DEGS TO GET TO THE W 270 DEG HDG ASAP. THE OTHER ACFT INVOLVED WAS TOLD TO TURN L TO A 090 DEG HDG IMMEDIATELY. RIGHT AFTER WE WERE GIVEN THE NEW HDG BY ATC; THE TFC APPEARED ON TCASII AND WE HEARD THE TCASII SAY 'TFC; TFC; MONITOR VERT SPD.' AS I WAS TURNING; I GLANCED AND SAW THE TFC ON TCASII. AS I CONTINUED THE TURN TO 270 DEGS; I ALSO TEMPORARILY LEVELED OFF TO AVOID DSNDING ANY FURTHER. ONCE I SAW WE WERE CLR OF THE TFC; I CONTINUED THE DSCNT TO FL280; WHICH WAS ABOUT 1 MIN LATER. WE WERE THEN TOLD TO PROCEED BACK ON COURSE. I BELIEVE THAT IT IS SOMETIMES HARD TO SEE TFC AT NIGHT BELOW YOU IN A DSCNT IF THERE ARE MANY LIGHTS ON THE GND; BECAUSE THE ACFT LIGHTS SOMETIMES BLEND IN WITH CITY LIGHTS. I CALLED ZKC WHEN WE GOT ON THE GND AND THEY TOLD ME THAT WE GOT AS CLOSE AS 1000 FT AND 3.7 MI.