To make complex queries in MongoDB using PowerShell, you can utilize the db.collection.find() method along with various operators to filter and manipulate the data. You can use comparison operators like $eq, $ne, $gt, $lt, $gte, $lte, logical operators like $and, $or, $not, and array operators like $in, $nin, $all to build complex queries. Additionally, you can also use regular expressions and aggregation pipelines to perform advanced querying operations.