Find indexof array of objects

The way that .NET by default compares things is just not as forgiving as PowerShell is!

[array]::IndexOf($array, $reference) will go through the array and return the current index when it encounters an item for which the following is true:

$item.Equals($reference)

... which is NOT necessarily the same as doing

$item -eq $reference

For simple values, like numbers and dates and so on, Equals() works exactly like -eq:

PS C:\> $a = 1
PS C:\> $b = 1
PS C:\> $a.Equals($b)  # $true

... which is the reason your first example works as expected!

For more complex objects though, Equals() works a bit differently. Both values MUST refer to the same object, it's not enough that they have similar or even identical values:

PS C:\> $a = New-Object object
PS C:\> $b = New-Object object
PS C:\> $a.Equals($b)    # $false

In the example above, $a and $b are similar (if not identical) - they're both empty objects - but they are not the same object.

Similarly, if we test with your input values, they aren't the same either:

PS C:\> $a = Get-Item "C:\"
PS C:\> $b = "C:\"
PS C:\> $a.Equals($b)    # $false

One of the reasons they can't be considered the same, as AdminOfThings excellently explains, is type mismatch - but PowerShell's comparison operators can help us here!

You'll notice that this works:

PS C:\> $a = Get-Item "C:\"
PS C:\> $b = "C:\"
PS C:\> $b -eq $a
True

That's because the behavior of -eq depends on the left-hand operand. In the example above, "C:\" is a string, so PowerShell converts $a to a string, and all of a sudden the comparison is more like "C:\".Equals("C:\")!

With this in mind, you could create your own Find-IndexOf function to do $reference -eq $item (or any other comparison mechanism you'd like) with a simple for() loop:

function Find-IndexOf
{
  param(
    [array]$Array,
    [object]$Value
  )

  for($idx = 0; $idx -lt $Array.Length; $idx++){
    if($Value -eq $Array[$idx]){
      return $idx
    }
  }

  return -1
}

Now you'd be able to do:

PS C:\> $array = @('','PowerShell is case-insensitive by default')
PS C:\> $value = 'POWERsheLL iS cASe-InSenSItIVe BY deFAuLt'
PS C:\> Find-IndexOf -Array $array -Value $value
1

Or:

PS C:\> $array = Get-ChildItem C:\images
PS C:\> $value = 'C:\images\image123.png'
PS C:\> Find-IndexOf -Array $array -Value $value
5

Adding comparison against a specific property on each of the array items (like the file's Name in your example), we end up with something like this:

function Find-IndexOf
{
  param(
    [array]$Array,
    [object]$Value,
    [string]$Property
  )

  if($Property){
    for($idx = 0; $idx -lt $Array.Length; $idx++){
      if($Value -eq $Array[$idx].$Property){
        return $idx
      }
    }
  }
  else {
    for($idx = 0; $idx -lt $Array.Length; $idx++){
      if($Value -eq $Array[$idx]){
        return $idx
      }
    }
  }

  return -1
}

Find-IndexOf -Array @(Get-ChildItem C:\images) -Value image123.png -Property Name