I agree with Mr. Knost's answer. I would add that a complex case adds 90 to 120 days (depending on if the defendant is in custody or out of custody) to the total amount of time that the prosecutor has to bring the case to trial.
Complex case designation is reserved for first degree murder cases, cases involving certain search warrants (wiretaps, etc.), and any other case that the Court believes is truly complex.
If a person is in jail, awaiting trial on a felony, normally the prosecution has 150 days from the arraignment to take it to trial. But in a complex case (if the Court grants the state's motion), the person in jail has to wait for 270 days from the arraignment.
Be aware, also, that during the process, if the defendant's lawyer agrees to "waive Rule 8 time" or anything to that effect, the process will take longer than 270 days, but the extension of time should be to the benefit of the defendant's case.