Does Power BI Support Complex Numbers?

The short answer is no, Power BI doesn't have a native data type for complex numbers. You can't simply feed it a column of values like "3 + 4i" and expect it to automatically perform calculations. However, that's far from the end of the story. With a bit of strategic data prep, you can absolutely work with and visualize complex numbers effectively inside Power BI. This article will show you exactly how to do it.

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We'll walk through two primary methods for handling complex numbers: first, by pre-processing them in Power Query, and second, by creating calculated columns using DAX. You will learn the exact steps to separate complex numbers into their real and imaginary parts, perform calculations like finding the magnitude, and then visualize the results on a scatter plot.

What Are Complex Numbers and Why Use Them in Data Analysis?

Before jumping into the solutions, let's have a quick refresher. A complex number is a number that includes both a real part and an imaginary part, usually written in the form a + bi.

• a is the real part.
• b is the imaginary part.
• i is the imaginary unit, which is defined as the square root of -1 (√-1).

While they might seem abstract, complex numbers are critical in many fields that use Power BI for analysis, particularly in various forms of engineering and science. They provide a simple way to model things that have both a magnitude (size) and a phase (direction or angle), such as:

• Electrical Engineering: Analyzing alternating current (AC) circuits, where they're used to represent impedance and voltage.
• Signal Processing: Applying Fourier transforms to break down signals (like sound or radio waves) into their constituent frequencies.
• Control Systems: Modeling system stability and response in mechanical engineering and robotics.
• Fluid Dynamics: Solving equations related to fluid flow around objects.

If you're working with data from any of these areas, you inevitably need a way to bring this information into your BI tools.

The Universal Strategy: Split Real and Imaginary Parts

Since Power BI can't understand "3 + 4i," the solution is to break it down into a format that Power BI does understand: regular numerical columns. The universal approach is to separate every complex number into two distinct columns:

1. A column for the real part (e.g., 3).
2. A column for the imaginary part (e.g., 4).

Once you have these two separate columns, you can perform virtually any complex number operation using standard arithmetic formulas. Now, let’s see how to implement this in Power BI.

Method 1: Using Power Query to Separate Complex Numbers

Power Query is the perfect place to handle data cleaning and transformation before it ever hits your data model. This approach is often the most efficient because the transformation only happens once during data refresh.

Let’s say you have source data in a CSV or Excel file that looks something like this:

Metric,Value,Impedance Measurement 1,150,3 + 4i Measurement 2,210,5 - 12i Measurement 3,180,-2 + 5i Measurement 4,225,8 + 0i

Here’s the step-by-step process to get this ready for analysis in Power BI's Power Query Editor.

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Step 1: Open the Power Query Editor and Spot the Problem

After loading your data, open the Power Query Editor. You’ll notice that Power BI likely classified your "Impedance" column as a Text data type. That’s because it sees non-numeric characters like "+", "-", and "i".

Step 2: Create Custom Columns for Real and Imaginary Parts

While "Split Column by Delimiter" can work for simple cases, it can fail when dealing with both plus and minus signs. A more robust way is to use custom columns with some conditional M language logic.

From the "Add Column" tab, click "Custom Column". Let's create the "RealPart" column first.

For the "RealPart," you need to find the space between the real and imaginary components. The formula below finds the position of the second operator (+ or -) if it exists and splits the string there.

let
    // Find the position of the "+" or "-". Look starting from the second character
    // to avoid splitting on a negative sign at the beginning.
    posPlus = Text.PositionOf([Impedance], "+", 1),
    posMinus = Text.PositionOf([Impedance], "-", 1),

    // Determine the split position, use a large number if no sign is found
    splitPos = if posPlus > 0 and posMinus > 0 then List.Min({posPlus, posMinus})
               else if posPlus > 0 then posPlus
               else if posMinus > 0 then posMinus
               else Text.Length([Impedance]),

    // Get the first part of the string
    realText = Text.Start([Impedance], splitPos)
in
    realText

Click OK. You will get a column with the real part extracted as text.

Now, create another custom column named "ImaginaryPart" using this slightly modified formula:

let
    // Find the position of the "+" or "-", starting from the second character.
    posPlus = Text.PositionOf([Impedance], "+", 1),
    posMinus = Text.PositionOf([Impedance], "-", 1),

    // Determine the split position
    splitPos = if posPlus > 0 and posMinus > 0 then List.Min({posPlus, posMinus})
               else if posPlus > 0 then posPlus
               else if posMinus > 0 then posMinus
               else -1,

    // Extract the imaginary part, handle cases without an imaginary part
    imaginaryText = if splitPos = -1 or Text.End([Impedance], 1) <> "i"
                      then "0"
                      else Text.Range([Impedance], splitPos, Text.Length([Impedance])),

    // Clean the extracted string by removing "i" and extra spaces
    cleanedText = Text.Replace(imaginaryText, "i", "")
in
    cleanedText

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Step 3: Clean and Convert Data Types

You now have two new columns, "RealPart" and "ImaginaryPart", but they're still text. Select both columns, go to the "Transform" tab, and change their Data Type to "Decimal Number". Finally, you can remove the original "Impedance" text column to keep your model clean.

Your table should now look like this, ready for calculations:

Method 2: Using DAX to Manage Complex Numbers

Alternatively, you can load the data as-is and use Data Analysis Expressions (DAX) to create calculated columns. This approach performs the calculation on-the-fly within the data model. It's useful if you get source data you can't or don't want to transform in Power Query.

Step 1: Load Data and Select Data View

Load your data with the text-based complex number column (e.g., 'Sheet1'[Impedance]) into Power BI. Then, navigate to the Data view on the left-hand panel.

Step 2: Create Calculated Columns with DAX

Select your table, then from the "Table tools" ribbon, click "New column."

To create the RealPart column, enter the following DAX formula. This formula searches for the "+" or "-" separator that is not at the very beginning of the string.

RealPart = 
VAR ComplexString = 'Sheet1'[Impedance]
// Find the position of the separator, if it's not the first character
VAR separatorPosPlus = FIND("+", ComplexString, 2, -1)
VAR separatorPosMinus = FIND("-", ComplexString, 2, -1)

// Determine the actual split position
VAR splitPos = 
    IF(separatorPosPlus > 0 && separatorPosMinus > 0,
        MIN(separatorPosPlus, separatorPosMinus),
        MAX(separatorPosPlus, separatorPosMinus)
    )

// Extract the real part text
VAR realText = 
    IF(splitPos > 0, 
        LEFT(ComplexString, splitPos - 1),
        // If no separator, the whole thing might be the real part
        IF(RIGHT(ComplexString, 1) = "i", "0", ComplexString)
    )

RETURN
    VALUE(TRIM(realText))

Next, create another new column named ImaginaryPart with this DAX formula:

ImaginaryPart = 
VAR ComplexString = 'Sheet1'[Impedance]
// Find the position of the separator that is not at the beginning
VAR separatorPosPlus = FIND("+", ComplexString, 2, -1)
VAR separatorPosMinus = FIND("-", ComplexString, 2, -1)

// Determine the actual split position as before
VAR splitPos = 
    IF(separatorPosPlus > 0 && separatorPosMinus > 0,
        MIN(separatorPosPlus, separatorPosMinus),
        MAX(separatorPosPlus, separatorPosMinus)
    )

// Extract the text for the imaginary part
VAR imaginaryText = 
    IF(splitPos > 0, 
        TRIM(SUBSTITUTE(MID(ComplexString, splitPos, 100), "i", "")),
        // Handle values like just "5i" or "-5i"
        TRIM(SUBSTITUTE(ComplexString, "i", ""))
    )

RETURN
    // Final check for values with real part "0" vs. imaginary part "0"
    IF(
        RIGHT(ComplexString, 1) = "i", 
        VALUE(imaginaryText), 
        0
    )

You’ll now have the same two numerical columns in your model, just created with a different method.

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Power Query vs. DAX: Which Should You Choose?

• Power Query: Choose for permanent transformation. The work happens during data refresh and is 'baked into' a new column. This is generally better for performance, as computations for calculated columns happen at refresh, but could potentially tax model memory if used extensively. It’s the standard for structuring source data correctly from the start.
• DAX Calculated Columns: Choose if you need calculations dependent on other elements within the loaded table or cannot edit the query itself. This method can feel more straightforward for users very comfortable with DAX. That said, heavy, row-by-row string manipulation in DAX can sometimes impact model size and performance.

Our recommendation for this specific task is to use Power Query. It is designed precisely for these kinds of data cleaning and formatting challenges.

Performing Calculations and Visualizing the Results

Now that you have your "RealPart" and "ImaginaryPart" columns, you can perform any required calculations. The most common is finding the magnitude (also known as the modulus), which represents the length of the vector in an Argand diagram. The formula is √(real² + imaginary²). Let’s create this as a DAX measure:

Average Magnitude = 
AVERAGEX(
    'Sheet1',
    SQRT('Sheet1'[RealPart]^2 + 'Sheet1'[ImaginaryPart]^2)
)

The best way to visualize complex numbers is on a Scatter Chart, which can act as a classic Argand diagram.

1. Add a Scatter Chart to your report canvas.
2. Drag 'RealPart' to the X Axis field.
3. Drag 'ImaginaryPart' to the Y Axis field.
4. Drag a unique identifier like 'Metric' to the Values field to plot each point individually.

You will now see each of your complex numbers plotted. Each point on this chart represents a magnitude and a phase angle, neatly visualizing your complex data in a simple, intuitive format.

Final Thoughts

While Power BI doesn’t natively support complex numbers, working around this limitation is straightforward by splitting them into their constituent real and imaginary parts. Using Power Query is typically the most efficient method for this transformation, as it handles the data cleaning at the source, letting you focus on the analysis in your DAX measures and visuals.

Unifying and cleaning data from different sources is often one of the most time-consuming parts of data analysis. Whether wrestling with complex data types or just trying to pull together metrics from a dozen marketing and sales platforms, it's easy to get bogged down before you start. At Graphed, we automate all that data connection and cleanup work so you can stop wrestling with formulas and just ask questions in plain English to get answers from all your connected sources in seconds.